LMFDB - Embedded newform 91.10.e.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(53,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	91.53
Dual form			91.10.e.a.79.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.4314 - 33.6561i) q^{2} +(-91.9975 + 159.344i) q^{3} +(-499.156 + 864.564i) q^{4} +(723.891 + 1253.82i) q^{5} +7150.55 q^{6} +(13.7108 - 6352.43i) q^{7} +18899.4 q^{8} +(-7085.57 - 12272.6i) q^{9} +O(q^{10})$	\(q+(-19.4314 - 33.6561i) q^{2} +(-91.9975 + 159.344i) q^{3} +(-499.156 + 864.564i) q^{4} +(723.891 + 1253.82i) q^{5} +7150.55 q^{6} +(13.7108 - 6352.43i) q^{7} +18899.4 q^{8} +(-7085.57 - 12272.6i) q^{9} +(28132.4 - 48726.7i) q^{10} +(6262.52 - 10847.0i) q^{11} +(-91842.2 - 159075. i) q^{12} -28561.0 q^{13} +(-214065. + 122975. i) q^{14} -266385. q^{15} +(-111674. - 193425. i) q^{16} +(-123171. + 213338. i) q^{17} +(-275365. + 476946. i) q^{18} +(81111.0 + 140488. i) q^{19} -1.44534e6 q^{20} +(1.01096e6 + 586593. i) q^{21} -486757. q^{22} +(-705399. - 1.22179e6i) q^{23} +(-1.73870e6 + 3.01152e6i) q^{24} +(-71473.3 + 123795. i) q^{25} +(554979. + 961252. i) q^{26} -1.01415e6 q^{27} +(5.48524e6 + 3.18271e6i) q^{28} -5.97356e6 q^{29} +(5.17622e6 + 8.96547e6i) q^{30} +(3.18900e6 - 5.52352e6i) q^{31} +(498300. - 863080. i) q^{32} +(1.15227e6 + 1.99579e6i) q^{33} +9.57352e6 q^{34} +(7.97471e6 - 4.58128e6i) q^{35} +1.41472e7 q^{36} +(6.63609e6 + 1.14940e7i) q^{37} +(3.15220e6 - 5.45976e6i) q^{38} +(2.62754e6 - 4.55103e6i) q^{39} +(1.36811e7 + 2.36964e7i) q^{40} +1.64998e7 q^{41} +(98039.4 - 4.54234e7i) q^{42} -2.06519e7 q^{43} +(6.25195e6 + 1.08287e7i) q^{44} +(1.02584e7 - 1.77680e7i) q^{45} +(-2.74137e7 + 4.74820e7i) q^{46} +(3.54652e6 + 6.14275e6i) q^{47} +4.10949e7 q^{48} +(-4.03532e7 - 174193. i) q^{49} +5.55530e6 q^{50} +(-2.26628e7 - 3.92532e7i) q^{51} +(1.42564e7 - 2.46928e7i) q^{52} +(-2.88279e7 + 4.99314e7i) q^{53} +(1.97064e7 + 3.41325e7i) q^{54} +1.81335e7 q^{55} +(259126. - 1.20057e8i) q^{56} -2.98480e7 q^{57} +(1.16074e8 + 2.01047e8i) q^{58} +(4.26717e7 - 7.39096e7i) q^{59} +(1.32968e8 - 2.30306e8i) q^{60} +(-4.01633e7 - 6.95649e7i) q^{61} -2.47867e8 q^{62} +(-7.80579e7 + 4.48424e7i) q^{63} -1.53085e8 q^{64} +(-2.06750e7 - 3.58102e7i) q^{65} +(4.47805e7 - 7.75620e7i) q^{66} +(1.17017e8 - 2.02680e8i) q^{67} +(-1.22963e8 - 2.12978e8i) q^{68} +2.59580e8 q^{69} +(-3.09148e8 - 1.79377e8i) q^{70} +3.31630e8 q^{71} +(-1.33913e8 - 2.31945e8i) q^{72} +(-831818. + 1.44075e6i) q^{73} +(2.57897e8 - 4.46690e8i) q^{74} +(-1.31507e7 - 2.27777e7i) q^{75} -1.61948e8 q^{76} +(-6.88190e7 - 3.99310e7i) q^{77} -2.04227e8 q^{78} +(2.41915e8 + 4.19009e8i) q^{79} +(1.61680e8 - 2.80037e8i) q^{80} +(2.32765e8 - 4.03161e8i) q^{81} +(-3.20614e8 - 5.55320e8i) q^{82} +1.53384e8 q^{83} +(-1.01178e9 + 5.81241e8i) q^{84} -3.56649e8 q^{85} +(4.01295e8 + 6.95064e8i) q^{86} +(5.49552e8 - 9.51853e8i) q^{87} +(1.18358e8 - 2.05002e8i) q^{88} +(-2.08953e8 - 3.61917e8i) q^{89} -7.97336e8 q^{90} +(-391593. + 1.81432e8i) q^{91} +1.40842e9 q^{92} +(5.86760e8 + 1.01630e9i) q^{93} +(1.37828e8 - 2.38724e8i) q^{94} +(-1.17431e8 + 2.03397e8i) q^{95} +(9.16846e7 + 1.58802e8i) q^{96} +3.96716e8 q^{97} +(7.78256e8 + 1.36152e9i) q^{98} -1.77494e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9}+O(q^{10}) $ 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9} + 16725 q^{10} + 117246 q^{11} + 79155 q^{12} - 1999270 q^{13} + 155800 q^{14} - 1075914 q^{15} - 1801693 q^{16} + 534494 q^{17} + 2034224 q^{18} - 1070554 q^{19} - 213462 q^{20} + 252483 q^{21} - 656508 q^{22} + 3982482 q^{23} - 8713082 q^{24} - 10791923 q^{25} - 1856465 q^{26} - 4695462 q^{27} + 43151747 q^{28} - 8248096 q^{29} + 7494360 q^{30} - 18116139 q^{31} + 23284165 q^{32} - 18685134 q^{33} - 35031796 q^{34} + 41739462 q^{35} + 69822756 q^{36} + 12174052 q^{37} - 86227130 q^{38} - 45752120 q^{40} - 14899440 q^{41} + 226294688 q^{42} - 100872292 q^{43} + 55709994 q^{44} - 128782765 q^{45} + 86862955 q^{46} - 15243502 q^{47} - 251600258 q^{48} + 168431298 q^{49} - 23415484 q^{50} + 89493887 q^{51} + 243711013 q^{52} + 42576150 q^{53} - 466420190 q^{54} - 72659096 q^{55} + 237491061 q^{56} - 533277320 q^{57} + 302514895 q^{58} + 40301350 q^{59} - 191686454 q^{60} + 9519912 q^{61} - 257610720 q^{62} - 292394291 q^{63} + 453888112 q^{64} + 60492198 q^{65} + 1445199979 q^{66} + 919692072 q^{67} - 220295462 q^{68} - 1381257496 q^{69} + 860352188 q^{70} - 811959580 q^{71} + 2266117080 q^{72} + 924540004 q^{73} - 727436321 q^{74} + 445426010 q^{75} + 649412196 q^{76} - 1151937348 q^{77} - 495761838 q^{78} + 1174788834 q^{79} + 2332520349 q^{80} - 800698791 q^{81} + 1124625342 q^{82} + 830514540 q^{83} + 1448184376 q^{84} - 1969339174 q^{85} + 1497823546 q^{86} + 721368044 q^{87} - 808482999 q^{88} - 1968216306 q^{89} + 777819470 q^{90} + 250308604 q^{91} - 4887921618 q^{92} + 853972744 q^{93} + 4664723138 q^{94} + 1357929150 q^{95} - 3736344295 q^{96} + 3467931764 q^{97} - 1557173329 q^{98} - 8781494080 q^{99}+O(q^{100}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9 + 16725 * q^10 + 117246 * q^11 + 79155 * q^12 - 1999270 * q^13 + 155800 * q^14 - 1075914 * q^15 - 1801693 * q^16 + 534494 * q^17 + 2034224 * q^18 - 1070554 * q^19 - 213462 * q^20 + 252483 * q^21 - 656508 * q^22 + 3982482 * q^23 - 8713082 * q^24 - 10791923 * q^25 - 1856465 * q^26 - 4695462 * q^27 + 43151747 * q^28 - 8248096 * q^29 + 7494360 * q^30 - 18116139 * q^31 + 23284165 * q^32 - 18685134 * q^33 - 35031796 * q^34 + 41739462 * q^35 + 69822756 * q^36 + 12174052 * q^37 - 86227130 * q^38 - 45752120 * q^40 - 14899440 * q^41 + 226294688 * q^42 - 100872292 * q^43 + 55709994 * q^44 - 128782765 * q^45 + 86862955 * q^46 - 15243502 * q^47 - 251600258 * q^48 + 168431298 * q^49 - 23415484 * q^50 + 89493887 * q^51 + 243711013 * q^52 + 42576150 * q^53 - 466420190 * q^54 - 72659096 * q^55 + 237491061 * q^56 - 533277320 * q^57 + 302514895 * q^58 + 40301350 * q^59 - 191686454 * q^60 + 9519912 * q^61 - 257610720 * q^62 - 292394291 * q^63 + 453888112 * q^64 + 60492198 * q^65 + 1445199979 * q^66 + 919692072 * q^67 - 220295462 * q^68 - 1381257496 * q^69 + 860352188 * q^70 - 811959580 * q^71 + 2266117080 * q^72 + 924540004 * q^73 - 727436321 * q^74 + 445426010 * q^75 + 649412196 * q^76 - 1151937348 * q^77 - 495761838 * q^78 + 1174788834 * q^79 + 2332520349 * q^80 - 800698791 * q^81 + 1124625342 * q^82 + 830514540 * q^83 + 1448184376 * q^84 - 1969339174 * q^85 + 1497823546 * q^86 + 721368044 * q^87 - 808482999 * q^88 - 1968216306 * q^89 + 777819470 * q^90 + 250308604 * q^91 - 4887921618 * q^92 + 853972744 * q^93 + 4664723138 * q^94 + 1357929150 * q^95 - 3736344295 * q^96 + 3467931764 * q^97 - 1557173329 * q^98 - 8781494080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−19.4314	−	33.6561i	−0.858753	−	1.48740i	−0.873119	−	0.487508i	$-0.837906\pi$
$2$	−19.4314	−	33.6561i	−0.858753	−	1.48740i	0.0143654	−	0.999897i	$-0.495427\pi$
$3$	−91.9975	+	159.344i	−0.655738	+	1.13577i	0.325970	+	0.945380i	$0.394309\pi$
$3$	−91.9975	+	159.344i	−0.655738	+	1.13577i	−0.981708	+	0.190391i	$0.939024\pi$
$4$	−499.156	+	864.564i	−0.974915	+	1.68860i
$5$	723.891	+	1253.82i	0.517974	+	0.897157i	0.999782	+	0.0208806i	$0.00664698\pi$
$5$	723.891	+	1253.82i	0.517974	+	0.897157i	−0.481808	+	0.876277i	$0.660020\pi$
$6$	7150.55			2.25247
$7$	13.7108	−	6352.43i	0.00215834	−	0.999998i
$7$	13.7108	−	6352.43i	0.00215834	−	0.999998i
$8$	18899.4			1.63134
$9$	−7085.57	−	12272.6i	−0.359984	−	0.623511i
$10$	28132.4	−	48726.7i	0.889624	−	1.54087i
$11$	6262.52	−	10847.0i	0.128968	−	0.223379i	−0.794309	−	0.607514i	$-0.792167\pi$
$11$	6262.52	−	10847.0i	0.128968	−	0.223379i	0.923277	+	0.384135i	$0.125500\pi$
$12$	−91842.2	−	159075.i	−1.27858	−	2.21456i
$13$	−28561.0			−0.277350
$13$	−28561.0			−0.277350
$14$	−214065.	+	122975.i	−1.48925	+	0.855541i
$15$	−266385.			−1.35862
$16$	−111674.	−	193425.i	−0.426002	−	0.737858i
$17$	−123171.	+	213338.i	−0.357675	+	0.619510i	−0.987572	−	0.157168i	$-0.949764\pi$
$17$	−123171.	+	213338.i	−0.357675	+	0.619510i	0.629897	+	0.776678i	$0.283097\pi$
$18$	−275365.	+	476946.i	−0.618276	+	1.07088i
$19$	81111.0	+	140488.i	0.142787	+	0.247314i	0.928545	−	0.371220i	$-0.121060\pi$
$19$	81111.0	+	140488.i	0.142787	+	0.247314i	−0.785758	+	0.618534i	$0.787727\pi$
$20$	−1.44534e6			−2.01992
$21$	1.01096e6	+	586593.i	1.13435	+	0.658188i
$22$	−486757.			−0.443007
$23$	−705399.	−	1.22179e6i	−0.525605	−	0.910375i	−0.999555	−	0.0298233i	$-0.990506\pi$
$23$	−705399.	−	1.22179e6i	−0.525605	−	0.910375i	0.473950	−	0.880552i	$-0.342828\pi$
$24$	−1.73870e6	+	3.01152e6i	−1.06973	+	1.85283i
$25$	−71473.3	+	123795.i	−0.0365943	+	0.0633833i
$26$	554979.	+	961252.i	0.238175	+	0.412532i
$27$	−1.01415e6			−0.367254
$28$	5.48524e6	+	3.18271e6i	1.68649	+	0.978557i
$29$	−5.97356e6			−1.56835			−0.784173	−	0.620542i	$-0.786913\pi$
$29$	−5.97356e6			−1.56835			−0.784173	+	0.620542i	$0.786913\pi$
$30$	5.17622e6	+	8.96547e6i	1.16672	+	2.02082i
$31$	3.18900e6	−	5.52352e6i	0.620194	−	1.07421i	−0.369256	−	0.929328i	$-0.620387\pi$
$31$	3.18900e6	−	5.52352e6i	0.620194	−	1.07421i	0.989449	−	0.144879i	$-0.0462793\pi$
$32$	498300.	−	863080.i	0.0840070	−	0.145504i
$33$	1.15227e6	+	1.99579e6i	0.169138	+	0.292956i
$34$	9.57352e6			1.22862
$35$	7.97471e6	−	4.58128e6i	0.898273	−	0.516037i
$36$	1.41472e7			1.40382
$37$	6.63609e6	+	1.14940e7i	0.582109	+	1.00824i	0.995229	+	0.0975663i	$0.0311058\pi$
$37$	6.63609e6	+	1.14940e7i	0.582109	+	1.00824i	−0.413120	+	0.910677i	$0.635561\pi$
$38$	3.15220e6	−	5.45976e6i	0.245238	−	0.424764i
$39$	2.62754e6	−	4.55103e6i	0.181869	−	0.315006i
$40$	1.36811e7	+	2.36964e7i	0.844991	+	1.46357i
$41$	1.64998e7			0.911910			0.455955	−	0.890003i	$-0.349298\pi$
$41$	1.64998e7			0.911910			0.455955	+	0.890003i	$0.349298\pi$
$42$	98039.4	−	4.54234e7i	0.00486159	−	2.25246i
$43$	−2.06519e7			−0.921197			−0.460599	−	0.887609i	$-0.652365\pi$
$43$	−2.06519e7			−0.921197			−0.460599	+	0.887609i	$0.652365\pi$
$44$	6.25195e6	+	1.08287e7i	0.251466	+	0.435551i
$45$	1.02584e7	−	1.77680e7i	0.372925	−	0.645925i
$46$	−2.74137e7	+	4.74820e7i	−0.902731	+	1.56358i
$47$	3.54652e6	+	6.14275e6i	0.106014	+	0.183621i	0.914152	−	0.405372i	$-0.132858\pi$
$47$	3.54652e6	+	6.14275e6i	0.106014	+	0.183621i	−0.808138	+	0.588993i	$0.799525\pi$
$48$	4.10949e7			1.11738
$49$	−4.03532e7	−	174193.i	−0.999991	−	0.00431667i
$50$	5.55530e6			0.125702
$51$	−2.26628e7	−	3.92532e7i	−0.469081	−	0.812473i
$52$	1.42564e7	−	2.46928e7i	0.270393	−	0.468334i
$53$	−2.88279e7	+	4.99314e7i	−0.501847	+	0.869224i	0.498151	+	0.867090i	$0.334013\pi$
$53$	−2.88279e7	+	4.99314e7i	−0.501847	+	0.869224i	−0.999998	+	0.00213397i	$0.999321\pi$
$54$	1.97064e7	+	3.41325e7i	0.315381	+	0.546256i
$55$	1.81335e7			0.267208
$56$	259126.	−	1.20057e8i	0.00352098	−	1.63133i
$57$	−2.98480e7			−0.374523
$58$	1.16074e8	+	2.01047e8i	1.34682	+	2.33277i
$59$	4.26717e7	−	7.39096e7i	0.458465	−	0.794084i	−0.540415	−	0.841398i	$-0.681733\pi$
$59$	4.26717e7	−	7.39096e7i	0.458465	−	0.794084i	0.998880	+	0.0473141i	$0.0150662\pi$
$60$	1.32968e8	−	2.30306e8i	1.32454	−	2.29417i
$61$	−4.01633e7	−	6.95649e7i	−0.371403	−	0.643289i	0.618379	−	0.785880i	$-0.287790\pi$
$61$	−4.01633e7	−	6.95649e7i	−0.371403	−	0.643289i	−0.989782	+	0.142592i	$0.954456\pi$
$62$	−2.47867e8			−2.13037
$63$	−7.80579e7	+	4.48424e7i	−0.624287	+	0.358638i
$64$	−1.53085e8			−1.14057
$65$	−2.06750e7	−	3.58102e7i	−0.143660	−	0.248827i
$66$	4.47805e7	−	7.75620e7i	0.290496	−	0.503155i
$67$	1.17017e8	−	2.02680e8i	0.709435	−	1.22878i	−0.255632	−	0.966774i	$-0.582284\pi$
$67$	1.17017e8	−	2.02680e8i	0.709435	−	1.22878i	0.965067	−	0.262003i	$-0.0843831\pi$
$68$	−1.22963e8	−	2.12978e8i	−0.697404	−	1.20794i
$69$	2.59580e8			1.37864
$70$	−3.09148e8	−	1.79377e8i	−1.53895	−	0.892948i
$71$	3.31630e8			1.54878			0.774392	−	0.632706i	$-0.218056\pi$
$71$	3.31630e8			1.54878			0.774392	+	0.632706i	$0.218056\pi$
$72$	−1.33913e8	−	2.31945e8i	−0.587256	−	1.01716i
$73$	−831818.	+	1.44075e6i	−0.00342827	+	0.00593795i	−0.867734	−	0.497028i	$-0.834425\pi$
$73$	−831818.	+	1.44075e6i	−0.00342827	+	0.00593795i	0.864306	+	0.502966i	$0.167758\pi$
$74$	2.57897e8	−	4.46690e8i	0.999777	−	1.73166i
$75$	−1.31507e7	−	2.27777e7i	−0.0479926	−	0.0831256i
$76$	−1.61948e8			−0.556820
$77$	−6.88190e7	−	3.99310e7i	−0.223100	−	0.129450i
$78$	−2.04227e8			−0.624722
$79$	2.41915e8	+	4.19009e8i	0.698780	+	1.21032i	0.968890	+	0.247493i	$0.0796068\pi$
$79$	2.41915e8	+	4.19009e8i	0.698780	+	1.21032i	−0.270109	+	0.962830i	$0.587060\pi$
$80$	1.61680e8	−	2.80037e8i	0.441316	−	0.764383i
$81$	2.32765e8	−	4.03161e8i	0.600807	−	1.04063i
$82$	−3.20614e8	−	5.55320e8i	−0.783106	−	1.35638i
$83$	1.53384e8			0.354756			0.177378	−	0.984143i	$-0.443239\pi$
$83$	1.53384e8			0.354756			0.177378	+	0.984143i	$0.443239\pi$
$84$	−1.01178e9	+	5.81241e8i	−2.21731	+	1.27379i
$85$	−3.56649e8			−0.741065
$86$	4.01295e8	+	6.95064e8i	0.791081	+	1.37019i
$87$	5.49552e8	−	9.51853e8i	1.02842	−	1.78128i
$88$	1.18358e8	−	2.05002e8i	0.210390	−	0.364407i
$89$	−2.08953e8	−	3.61917e8i	−0.353016	−	0.611441i	0.633761	−	0.773529i	$-0.281510\pi$
$89$	−2.08953e8	−	3.61917e8i	−0.353016	−	0.611441i	−0.986776	+	0.162088i	$0.948177\pi$
$90$	−7.97336e8			−1.28100
$91$	−391593.	+	1.81432e8i	−0.000598616	+	0.277349i
$92$	1.40842e9			2.04968
$93$	5.86760e8	+	1.01630e9i	0.813369	+	1.40880i
$94$	1.37828e8	−	2.38724e8i	0.182079	−	0.315371i
$95$	−1.17431e8	+	2.03397e8i	−0.147920	+	0.256205i
$96$	9.16846e7	+	1.58802e8i	0.110173	+	0.190826i
$97$	3.96716e8			0.454995			0.227498	−	0.973779i	$-0.426946\pi$
$97$	3.96716e8			0.454995			0.227498	+	0.973779i	$0.426946\pi$
$98$	7.78256e8	+	1.36152e9i	0.852325	+	1.49110i
$99$	−1.77494e8			−0.185706
$100$	−7.13527e7	−	1.23587e8i	−0.0713527	−	0.123587i
$101$	6.59056e8	−	1.14152e9i	0.630197	−	1.09153i	−0.357315	−	0.933984i	$-0.616308\pi$
$101$	6.59056e8	−	1.14152e9i	0.630197	−	1.09153i	0.987511	−	0.157548i	$-0.0503591\pi$
$102$	−8.80740e8	+	1.52549e9i	−0.805651	+	1.39543i
$103$	2.13415e7	+	3.69645e7i	0.0186834	+	0.0323607i	0.875216	−	0.483732i	$-0.160719\pi$
$103$	2.13415e7	+	3.69645e7i	0.0186834	+	0.0323607i	−0.856533	+	0.516093i	$0.827386\pi$
$104$	−5.39787e8			−0.452452
$105$	−3.65233e6	+	1.69219e9i	−0.00293237	+	1.35862i
$106$	2.24066e9			1.72385
$107$	2.44640e7	+	4.23728e7i	0.0180426	+	0.0312508i	0.874906	−	0.484293i	$-0.160923\pi$
$107$	2.44640e7	+	4.23728e7i	0.0180426	+	0.0312508i	−0.856863	+	0.515544i	$0.827590\pi$
$108$	5.06221e8	−	8.76801e8i	0.358041	−	0.620146i
$109$	1.89970e8	−	3.29037e8i	0.128904	−	0.223268i	−0.794348	−	0.607462i	$-0.792188\pi$
$109$	1.89970e8	−	3.29037e8i	0.128904	−	0.223268i	0.923252	+	0.384195i	$0.125521\pi$
$110$	−3.52359e8	−	6.10304e8i	−0.229466	−	0.397447i
$111$	−2.44201e9			−1.52684
$112$	−1.23025e9	+	7.06750e8i	−0.738776	+	0.424409i
$113$	1.94722e9			1.12347			0.561736	−	0.827317i	$-0.310134\pi$
$113$	1.94722e9			1.12347			0.561736	+	0.827317i	$0.310134\pi$
$114$	5.79988e8	+	1.00457e9i	0.321623	+	0.557068i
$115$	1.02126e9	−	1.76888e9i	0.544500	−	0.943101i
$116$	2.98174e9	−	5.16452e9i	1.52900	−	2.64831i
$117$	2.02371e8	+	3.50517e8i	0.0998417	+	0.172931i
$118$	−3.31668e9			−1.57483
$119$	1.35353e9	+	7.85360e8i	0.618737	+	0.359011i
$120$	−5.03452e9			−2.21637
$121$	1.10054e9	+	1.90618e9i	0.466734	+	0.808408i
$122$	−1.56086e9	+	2.70348e9i	−0.637887	+	1.10485i
$123$	−1.51794e9	+	2.62915e9i	−0.597974	+	1.03572i
$124$	3.18362e9	+	5.51419e9i	1.20927	+	2.09452i
$125$	2.62074e9			0.960129
$126$	3.02599e9	+	1.75578e9i	1.06955	+	0.620585i
$127$	−5.26587e8			−0.179619			−0.0898097	−	0.995959i	$-0.528626\pi$
$127$	−5.26587e8			−0.179619			−0.0898097	+	0.995959i	$0.528626\pi$
$128$	2.71952e9	+	4.71034e9i	0.895461	+	1.55098i
$129$	1.89993e9	−	3.29077e9i	0.604064	−	1.04627i
$130$	−8.03489e8	+	1.39168e9i	−0.246737	+	0.427362i
$131$	6.46945e8	+	1.12054e9i	0.191931	+	0.332435i	0.945890	−	0.324487i	$-0.105192\pi$
$131$	6.46945e8	+	1.12054e9i	0.191931	+	0.332435i	−0.753959	+	0.656922i	$0.771858\pi$
$132$	−2.30066e9			−0.659582
$133$	8.93555e8	−	5.13326e8i	0.247622	−	0.142253i
$134$	−9.09521e9			−2.43692
$135$	−7.34136e8	−	1.27156e9i	−0.190228	−	0.329485i
$136$	−2.32786e9	+	4.03197e9i	−0.583488	+	1.01063i
$137$	−2.65452e9	+	4.59776e9i	−0.643789	+	1.11507i	0.340791	+	0.940139i	$0.389305\pi$
$137$	−2.65452e9	+	4.59776e9i	−0.643789	+	1.11507i	−0.984580	+	0.174936i	$0.944028\pi$
$138$	−5.04399e9	−	8.73645e9i	−1.18391	−	2.05059i
$139$	3.00593e9			0.682987			0.341493	−	0.939884i	$-0.389067\pi$
$139$	3.00593e9			0.682987			0.341493	+	0.939884i	$0.389067\pi$
$140$	−1.98167e7	+	9.18142e9i	−0.00435968	+	2.01992i
$141$	−1.30508e9			−0.278069
$142$	−6.44402e9	−	1.11614e10i	−1.33002	−	2.30367i
$143$	−1.78864e8	+	3.09801e8i	−0.0357693	+	0.0619542i
$144$	−1.58255e9	+	2.74105e9i	−0.306708	+	0.531235i
$145$	−4.32420e9	−	7.48974e9i	−0.812363	−	1.40705i
$146$	6.46535e7			0.0117762
$147$	3.74015e9	−	6.41403e9i	0.660635	−	1.13293i
$148$	−1.32498e10			−2.27003
$149$	−1.96083e9	−	3.39626e9i	−0.325914	−	0.564499i	0.655783	−	0.754949i	$-0.272339\pi$
$149$	−1.96083e9	−	3.39626e9i	−0.325914	−	0.564499i	−0.981697	+	0.190450i	$0.939005\pi$
$150$	−5.11073e8	+	8.85205e8i	−0.0824276	+	0.142769i
$151$	4.72635e9	−	8.18628e9i	0.739826	−	1.28142i	−0.212748	−	0.977107i	$-0.568241\pi$
$151$	4.72635e9	−	8.18628e9i	0.739826	−	1.28142i	0.952573	−	0.304309i	$-0.0984255\pi$
$152$	1.53295e9	+	2.65515e9i	0.232934	+	0.403453i
$153$	3.49095e9			0.515029
$154$	−6.67381e6	+	3.09209e9i	−0.000956160	+	0.443006i
$155$	9.23396e9			1.28498
$156$	2.62311e9	+	4.54335e9i	0.354613	+	0.614208i
$157$	1.05725e9	−	1.83120e9i	0.138876	−	0.240541i	−0.788195	−	0.615425i	$-0.788984\pi$
$157$	1.05725e9	−	1.83120e9i	0.138876	−	0.240541i	0.927072	+	0.374885i	$0.122318\pi$
$158$	9.40147e9	−	1.62838e10i	1.20016	−	2.07874i
$159$	−5.30418e9	−	9.18712e9i	−0.658160	−	1.13997i
$160$	1.44286e9			0.174054
$161$	−7.77100e9	+	4.46425e9i	−0.911507	+	0.523639i
$162$	−1.80918e10			−2.06378
$163$	7.62743e9	+	1.32111e10i	0.846319	+	1.46587i	0.884471	+	0.466595i	$0.154519\pi$
$163$	7.62743e9	+	1.32111e10i	0.846319	+	1.46587i	−0.0381525	+	0.999272i	$0.512147\pi$
$164$	−8.23600e9	+	1.42652e10i	−0.889035	+	1.53985i
$165$	−1.66824e9	+	2.88947e9i	−0.175219	+	0.303488i
$166$	−2.98047e9	−	5.16232e9i	−0.304648	−	0.527665i
$167$	−9.60795e9			−0.955887			−0.477943	−	0.878391i	$-0.658618\pi$
$167$	−9.60795e9			−0.955887			−0.477943	+	0.878391i	$0.658618\pi$
$168$	1.91066e10	+	1.10863e10i	1.85051	+	1.07373i
$169$	8.15731e8			0.0769231
$170$	6.93018e9	+	1.20034e10i	0.636392	+	1.10226i
$171$	1.14944e9	−	1.99088e9i	0.102802	−	0.178059i
$172$	1.03085e10	−	1.78549e10i	0.898089	−	1.55554i
$173$	9.35234e9	+	1.61987e10i	0.793803	+	1.37491i	0.923596	+	0.383367i	$0.125235\pi$
$173$	9.35234e9	+	1.61987e10i	0.793803	+	1.37491i	−0.129793	+	0.991541i	$0.541431\pi$
$174$	−4.27142e10			−3.53265
$175$	7.85422e8	+	4.55727e8i	0.0633041	+	0.0367311i
$176$	−2.79744e9			−0.219763
$177$	7.85138e9	+	1.35990e10i	0.601265	+	1.04142i
$178$	−8.12049e9	+	1.40651e10i	−0.606307	+	1.05015i
$179$	5.25967e9	−	9.11001e9i	0.382930	−	0.663254i	−0.608550	−	0.793516i	$-0.708248\pi$
$179$	5.25967e9	−	9.11001e9i	0.382930	−	0.663254i	0.991480	+	0.130261i	$0.0415817\pi$
$180$	1.02411e10	+	1.77380e10i	0.727140	+	1.25944i
$181$	1.94199e10			1.34491			0.672454	−	0.740139i	$-0.265240\pi$
$181$	1.94199e10			1.34491			0.672454	+	0.740139i	$0.265240\pi$
$182$	6.11390e9	−	3.51229e9i	0.413045	−	0.237284i
$183$	1.47797e10			0.974172
$184$	−1.33317e10	−	2.30911e10i	−0.857440	−	1.48513i
$185$	−9.60761e9	+	1.66409e10i	−0.603035	+	1.04449i
$186$	2.28031e10	−	3.94962e10i	1.39697	−	2.41962i
$187$	1.54272e9	+	2.67207e9i	0.0922571	+	0.159794i
$188$	−7.08107e9			−0.413417
$189$	−1.39048e7	+	6.44234e9i	−0.000792660	+	0.367253i
$190$	9.12738e9			0.508107
$191$	9.24464e9	+	1.60122e10i	0.502620	+	0.870564i	0.999995	+	0.00302834i	$0.000963953\pi$
$191$	9.24464e9	+	1.60122e10i	0.502620	+	0.870564i	−0.497375	+	0.867536i	$0.665703\pi$
$192$	1.40834e10	−	2.43932e10i	0.747915	−	1.29543i
$193$	1.10070e10	−	1.90647e10i	0.571033	−	0.989058i	−0.425427	−	0.904993i	$-0.639876\pi$
$193$	1.10070e10	−	1.90647e10i	0.571033	−	0.989058i	0.996460	−	0.0840656i	$-0.0267905\pi$
$194$	−7.70873e9	−	1.33519e10i	−0.390729	−	0.676762i
$195$	7.60821e9			0.376814
$196$	2.02932e10	−	3.48010e10i	0.982195	−	1.68438i
$197$	−5.18355e9			−0.245205			−0.122603	−	0.992456i	$-0.539124\pi$
$197$	−5.18355e9			−0.245205			−0.122603	+	0.992456i	$0.539124\pi$
$198$	3.44895e9	+	5.97376e9i	0.159476	+	0.276220i
$199$	9.43644e9	−	1.63444e10i	0.426550	−	0.738806i	−0.570014	−	0.821635i	$-0.693062\pi$
$199$	9.43644e9	−	1.63444e10i	0.426550	−	0.738806i	0.996564	+	0.0828293i	$0.0263956\pi$
$200$	−1.35081e9	+	2.33966e9i	−0.0596977	+	0.103400i
$201$	2.15306e10	+	3.72920e10i	0.930407	+	1.61151i
$202$	−5.12254e10			−2.16473
$203$	−8.19020e7	+	3.79466e10i	−0.00338503	+	1.56834i
$204$	4.52492e10			1.82926
$205$	1.19441e10	+	2.06877e10i	0.472346	+	0.818127i
$206$	8.29388e8	−	1.43654e9i	0.0320889	−	0.0555796i
$207$	−9.99632e9	+	1.73141e10i	−0.378419	+	0.655442i
$208$	3.18952e9	+	5.52441e9i	0.118152	+	0.204645i
$209$	2.03184e9			0.0736598
$210$	5.70235e10	−	3.27586e10i	2.02333	−	1.16236i
$211$	−2.35997e10			−0.819664			−0.409832	−	0.912161i	$-0.634413\pi$
$211$	−2.35997e10			−0.819664			−0.409832	+	0.912161i	$0.634413\pi$
$212$	−2.87792e10	−	4.98471e10i	−0.978516	−	1.69484i
$213$	−3.05091e10	+	5.28433e10i	−1.01560	+	1.75907i
$214$	9.50737e8	−	1.64672e9i	0.0309883	−	0.0536734i
$215$	−1.49497e10	−	2.58937e10i	−0.477156	−	0.826459i
$216$	−1.91669e10			−0.599116
$217$	−3.50440e10	−	2.03337e10i	−1.07287	−	0.622511i
$218$	−1.47655e10			−0.442786
$219$	−1.53050e8	−	2.65091e8i	−0.00449610	−	0.00778747i
$220$	−9.05146e9	+	1.56776e10i	−0.260505	+	0.451209i
$221$	3.51788e9	−	6.09315e9i	0.0992011	−	0.171821i
$222$	4.74517e10	+	8.21887e10i	1.31118	+	2.27104i
$223$	2.30112e10			0.623113			0.311556	−	0.950228i	$-0.399150\pi$
$223$	2.30112e10			0.623113			0.311556	+	0.950228i	$0.399150\pi$
$224$	−5.47583e9	−	3.17725e9i	−0.145323	−	0.0843209i
$225$	2.02572e9			0.0526936
$226$	−3.78372e10	−	6.55359e10i	−0.964785	−	1.67106i
$227$	−1.23848e10	+	2.14510e10i	−0.309579	+	0.536206i	−0.978270	−	0.207334i	$-0.933521\pi$
$227$	−1.23848e10	+	2.14510e10i	−0.309579	+	0.536206i	0.668691	+	0.743540i	$0.266855\pi$
$228$	1.48988e10	−	2.58055e10i	0.365128	−	0.632421i
$229$	−1.98474e10	−	3.43767e10i	−0.476918	−	0.826046i	0.522732	−	0.852497i	$-0.324913\pi$
$229$	−1.98474e10	−	3.43767e10i	−0.476918	−	0.826046i	−0.999650	+	0.0264508i	$0.991579\pi$
$230$	−7.93782e10			−1.87036
$231$	1.26939e10	−	7.29237e9i	0.293321	−	0.168506i
$232$	−1.12897e11			−2.55850
$233$	2.26592e10	+	3.92468e10i	0.503666	+	0.872375i	0.999991	+	0.00423812i	$0.00134904\pi$
$233$	2.26592e10	+	3.92468e10i	0.503666	+	0.872375i	−0.496325	+	0.868137i	$0.665318\pi$
$234$	7.86469e9	−	1.36220e10i	0.171479	−	0.297010i
$235$	−5.13459e9	+	8.89337e9i	−0.109825	+	0.190222i
$236$	4.25997e10	+	7.37848e10i	0.893928	+	1.54833i
$237$	−8.90222e10			−1.83287
$238$	1.31260e8	−	6.08151e10i	0.00265177	−	1.22861i
$239$	5.55464e10			1.10120			0.550599	−	0.834770i	$-0.314399\pi$
$239$	5.55464e10			1.10120			0.550599	+	0.834770i	$0.314399\pi$
$240$	2.97482e10	+	5.15254e10i	0.578776	+	1.00247i
$241$	3.23254e10	−	5.59892e10i	0.617259	−	1.06912i	−0.372725	−	0.927942i	$-0.621577\pi$
$241$	3.23254e10	−	5.59892e10i	0.617259	−	1.06912i	0.989984	−	0.141182i	$-0.0450901\pi$
$242$	4.27698e10	−	7.40795e10i	0.801620	−	1.38845i
$243$	3.28468e10	+	5.68923e10i	0.604317	+	1.04671i
$244$	8.01911e10			1.44834
$245$	−2.89929e10	−	5.07216e10i	−0.514097	−	0.899385i
$246$	1.17983e11			2.05405
$247$	−2.31661e9	−	4.01249e9i	−0.0396020	−	0.0685926i
$248$	6.02704e10	−	1.04391e11i	1.01175	−	1.75239i
$249$	−1.41110e10	+	2.44409e10i	−0.232627	+	0.402921i
$250$	−5.09246e10	−	8.82040e10i	−0.824514	−	1.42810i
$251$	−9.68039e10			−1.53943			−0.769717	−	0.638385i	$-0.779603\pi$
$251$	−9.68039e10			−1.53943			−0.769717	+	0.638385i	$0.779603\pi$
$252$	1.93969e8	−	8.98694e10i	0.00302991	−	1.40381i
$253$	−1.76703e10			−0.271145
$254$	1.02323e10	+	1.77229e10i	0.154249	+	0.267167i
$255$	3.28108e10	−	5.68300e10i	0.485944	−	0.841680i
$256$	6.64982e10	−	1.15178e11i	0.967676	−	1.67606i
$257$	−5.02042e10	−	8.69562e10i	−0.717862	−	1.24337i	−0.961845	−	0.273594i	$-0.911788\pi$
$257$	−5.02042e10	−	8.69562e10i	−0.717862	−	1.24337i	0.243984	−	0.969779i	$-0.421546\pi$
$258$	−1.47673e11			−2.07497
$259$	7.31062e10	−	4.19977e10i	1.00950	−	0.579932i
$260$	4.12803e10			0.560226
$261$	4.23261e10	+	7.33109e10i	0.564580	+	0.977882i
$262$	2.51420e10	−	4.35473e10i	0.329644	−	0.570959i
$263$	1.05235e10	−	1.82272e10i	0.135631	−	0.234919i	−0.790208	−	0.612839i	$-0.790027\pi$
$263$	1.05235e10	−	1.82272e10i	0.135631	−	0.234919i	0.925838	+	0.377920i	$0.123361\pi$
$264$	2.17773e10	+	3.77194e10i	0.275922	+	0.477911i
$265$	−8.34729e10			−1.03977
$266$	−3.46396e10	−	2.00990e10i	−0.424234	−	0.246154i
$267$	7.68927e10			0.925943
$268$	1.16820e11	+	2.02338e11i	1.38328	+	2.39591i
$269$	−6.78857e10	+	1.17581e11i	−0.790484	+	1.36916i	0.135184	+	0.990821i	$0.456837\pi$
$269$	−6.78857e10	+	1.17581e11i	−0.790484	+	1.36916i	−0.925668	+	0.378338i	$0.876496\pi$
$270$	−2.85306e10	+	4.94164e10i	−0.326718	+	0.565892i
$271$	−5.50323e10	−	9.53187e10i	−0.619806	−	1.07353i	−0.989521	−	0.144390i	$-0.953878\pi$
$271$	−5.50323e10	−	9.53187e10i	−0.619806	−	1.07353i	0.369715	−	0.929145i	$-0.379455\pi$
$272$	5.50199e10			0.609481
$273$	−2.88741e10	−	1.67537e10i	−0.314613	−	0.182548i
$274$	2.06324e11			2.21142
$275$	8.95206e8	+	1.55054e9i	0.00943900	+	0.0163488i
$276$	−1.29571e11	+	2.24423e11i	−1.34405	+	2.32797i
$277$	−1.89213e9	+	3.27726e9i	−0.0193104	+	0.0334466i	−0.875519	−	0.483183i	$-0.839480\pi$
$277$	−1.89213e9	+	3.27726e9i	−0.0193104	+	0.0334466i	0.856209	+	0.516630i	$0.172814\pi$
$278$	−5.84093e10	−	1.01168e11i	−0.586517	−	1.01588i
$279$	−9.03837e10			−0.893040
$280$	1.50717e11	−	8.65836e10i	1.46539	−	0.841830i
$281$	1.38976e10			0.132973			0.0664864	−	0.997787i	$-0.478821\pi$
$281$	1.38976e10			0.132973			0.0664864	+	0.997787i	$0.478821\pi$
$282$	2.53596e10	+	4.39241e10i	0.238793	+	0.413601i
$283$	−5.98449e9	+	1.03654e10i	−0.0554611	+	0.0960614i	−0.892423	−	0.451200i	$-0.850996\pi$
$283$	−5.98449e9	+	1.03654e10i	−0.0554611	+	0.0960614i	0.836962	+	0.547261i	$0.184330\pi$
$284$	−1.65535e11	+	2.86715e11i	−1.50993	+	2.61528i
$285$	−2.16067e10	−	3.74239e10i	−0.193993	−	0.336006i
$286$	1.39023e10			0.122868
$287$	2.26225e8	−	1.04814e11i	0.00196821	−	0.911908i
$288$	−1.41230e10			−0.120965
$289$	2.89518e10	+	5.01460e10i	0.244138	+	0.422859i
$290$	−1.68050e11	+	2.91072e11i	−1.39524	+	2.41662i
$291$	−3.64969e10	+	6.32144e10i	−0.298358	+	0.516771i
$292$	−8.30415e8	−	1.43832e9i	−0.00668455	−	0.0115780i
$293$	7.38699e10			0.585549			0.292775	−	0.956182i	$-0.405421\pi$
$293$	7.38699e10			0.585549			0.292775	+	0.956182i	$0.405421\pi$
$294$	−2.88548e11	−	1.24558e9i	−2.25245	−	0.00972317i
$295$	1.23559e11			0.949892
$296$	1.25418e11	+	2.17231e11i	0.949617	+	1.64479i
$297$	−6.35116e9	+	1.10005e10i	−0.0473640	+	0.0820369i
$298$	−7.62034e10	+	1.31988e11i	−0.559759	+	0.969531i
$299$	2.01469e10	+	3.48955e10i	0.145777	+	0.252493i
$300$	2.62571e10			0.187155
$301$	−2.83153e8	+	1.31190e11i	−0.00198826	+	0.921195i
$302$	−3.67358e11			−2.54131
$303$	1.21263e11	+	2.10034e11i	0.826488	+	1.43152i
$304$	1.81160e10	−	3.13778e10i	0.121655	−	0.210713i
$305$	5.81477e10	−	1.00715e11i	0.384754	−	0.666414i
$306$	−6.78339e10	−	1.17492e11i	−0.442283	−	0.766056i
$307$	1.80148e11			1.15746			0.578731	−	0.815518i	$-0.303548\pi$
$307$	1.80148e11			1.15746			0.578731	+	0.815518i	$0.303548\pi$
$308$	6.88743e10	−	3.95666e10i	0.436093	−	0.250525i
$309$	−7.85344e9			−0.0490057
$310$	−1.79428e11	−	3.10779e11i	−1.10348	−	1.91128i
$311$	−1.61437e11	+	2.79617e11i	−0.978547	+	1.69489i	−0.310851	+	0.950459i	$0.600614\pi$
$311$	−1.61437e11	+	2.79617e11i	−0.978547	+	1.69489i	−0.667696	+	0.744434i	$0.732719\pi$
$312$	4.96590e10	−	8.60120e10i	0.296690	−	0.513882i
$313$	−1.49581e11	−	2.59082e11i	−0.880901	−	1.52577i	−0.850340	−	0.526233i	$-0.823604\pi$
$313$	−1.49581e11	−	2.59082e11i	−0.880901	−	1.52577i	−0.0305609	−	0.999533i	$-0.509729\pi$
$314$	−8.21750e10			−0.477042
$315$	−1.12729e11	−	6.54092e10i	−0.645119	−	0.374318i
$316$	−4.83013e11			−2.72500
$317$	−2.27313e10	−	3.93718e10i	−0.126432	−	0.218987i	0.795860	−	0.605481i	$-0.207019\pi$
$317$	−2.27313e10	−	3.93718e10i	−0.126432	−	0.218987i	−0.922292	+	0.386494i	$0.873686\pi$
$318$	−2.06135e11	+	3.57037e11i	−1.13039	+	1.95790i
$319$	−3.74095e10	+	6.47952e10i	−0.202267	+	0.350336i
$320$	−1.10817e11	−	1.91940e11i	−0.590786	−	1.02327i
$321$	−9.00249e9			−0.0473249
$322$	3.01250e11	+	1.74795e11i	1.56162	+	0.906103i
$323$	−3.99621e10			−0.204285
$324$	2.32372e11	+	4.02480e11i	1.17147	+	2.02905i
$325$	2.04135e9	−	3.53572e9i	0.0101494	−	0.0175794i
$326$	2.96423e11	−	5.13419e11i	1.45356	−	2.51764i
$327$	3.49535e10	+	6.05412e10i	0.169054	+	0.292810i
$328$	3.11838e11			1.48763
$329$	3.90701e10	−	2.24448e10i	0.183850	−	0.105617i
$330$	1.29665e11			0.601878
$331$	1.28739e11	+	2.22982e11i	0.589500	+	1.02104i	0.994298	+	0.106638i	$0.0340087\pi$
$331$	1.28739e11	+	2.22982e11i	0.589500	+	1.02104i	−0.404797	+	0.914406i	$0.632658\pi$
$332$	−7.65627e10	+	1.32611e11i	−0.345857	+	0.599041i
$333$	9.40410e10	−	1.62884e11i	0.419101	−	0.725904i
$334$	1.86696e11	+	3.23366e11i	0.820871	+	1.42179i
$335$	3.38830e11			1.46988
$336$	5.63442e8	−	2.61053e11i	0.00241170	−	1.11738i
$337$	1.15860e11			0.489327			0.244664	−	0.969608i	$-0.421322\pi$
$337$	1.15860e11			0.489327			0.244664	+	0.969608i	$0.421322\pi$
$338$	−1.58508e10	−	2.74543e10i	−0.0660579	−	0.114416i
$339$	−1.79139e11	+	3.10279e11i	−0.736703	+	1.27601i
$340$	1.78024e11	−	3.08346e11i	0.722475	−	1.25136i
$341$	−3.99424e10	−	6.91823e10i	−0.159970	−	0.277077i
$342$	−8.93405e10			−0.353127
$343$	−1.65982e9	+	2.56339e11i	−0.00647498	+	0.999979i
$344$	−3.90310e11			−1.50278
$345$	1.87907e11	+	3.25465e11i	0.714098	+	1.23685i
$346$	3.63458e11	−	6.29527e11i	1.36336	−	2.36141i
$347$	4.95129e10	−	8.57589e10i	0.183331	−	0.317539i	−0.759682	−	0.650295i	$-0.774645\pi$
$347$	4.95129e10	−	8.57589e10i	0.183331	−	0.317539i	0.943013	+	0.332756i	$0.107979\pi$
$348$	5.48625e11	+	9.50246e11i	2.00525	+	3.47320i
$349$	3.20311e11			1.15573			0.577865	−	0.816132i	$-0.303886\pi$
$349$	3.20311e11			1.15573			0.577865	+	0.816132i	$0.303886\pi$
$350$	7.61673e7	−	3.52897e10i	0.000271308	−	0.125702i
$351$	2.89652e10			0.101858
$352$	−6.24122e9	−	1.08101e10i	−0.0216684	−	0.0375308i
$353$	−5.81078e10	+	1.00646e11i	−0.199181	+	0.344992i	−0.948263	−	0.317485i	$-0.897162\pi$
$353$	−5.81078e10	+	1.00646e11i	−0.199181	+	0.344992i	0.749082	+	0.662477i	$0.230495\pi$
$354$	3.05126e11	−	5.28494e11i	1.03268	−	1.78865i
$355$	2.40064e11	+	4.15803e11i	0.802230	+	1.38950i
$356$	4.17201e11			1.37664
$357$	−2.49664e11	+	1.43426e11i	−0.813483	+	0.467327i
$358$	−4.08810e11			−1.31537
$359$	−1.50519e11	−	2.60706e11i	−0.478261	−	0.828373i	0.521428	−	0.853295i	$-0.325399\pi$
$359$	−1.50519e11	−	2.60706e11i	−0.478261	−	0.828373i	−0.999689	+	0.0249224i	$0.992066\pi$
$360$	1.93877e11	−	3.35805e11i	0.608367	−	1.05372i
$361$	1.48186e11	−	2.56665e11i	0.459224	−	0.795399i
$362$	−3.77355e11	−	6.53598e11i	−1.15495	−	2.00042i
$363$	−4.04986e11			−1.22422
$364$	−1.56664e11	−	9.09014e10i	−0.467749	−	0.271403i
$365$	−2.40858e9			−0.00710303
$366$	−2.87190e11	−	4.97427e11i	−0.836573	−	1.44899i
$367$	3.12636e11	−	5.41501e11i	0.899583	−	1.55812i	0.0715548	−	0.997437i	$-0.477204\pi$
$367$	3.12636e11	−	5.41501e11i	0.899583	−	1.55812i	0.828028	−	0.560687i	$-0.189463\pi$
$368$	−1.57549e11	+	2.72884e11i	−0.447818	+	0.775644i
$369$	−1.16911e11	−	2.02495e11i	−0.328274	−	0.568586i
$370$	7.46756e11			2.07143
$371$	3.16790e11	+	1.83812e11i	0.868139	+	0.503722i
$372$	−1.17154e12			−3.17186
$373$	−1.36990e11	−	2.37273e11i	−0.366437	−	0.634687i	0.622569	−	0.782565i	$-0.286089\pi$
$373$	−1.36990e11	−	2.37273e11i	−0.366437	−	0.634687i	−0.989006	+	0.147878i	$0.952756\pi$
$374$	5.99543e10	−	1.03844e11i	0.158452	−	0.274447i
$375$	−2.41102e11	+	4.17600e11i	−0.629593	+	1.09049i
$376$	6.70272e10	+	1.16095e11i	0.172944	+	0.299548i
$377$	1.70611e11			0.434981
$378$	2.17094e11	−	1.24716e11i	0.546935	−	0.314201i
$379$	−4.55969e11			−1.13517			−0.567583	−	0.823316i	$-0.692121\pi$
$379$	−4.55969e11			−1.13517			−0.567583	+	0.823316i	$0.692121\pi$
$380$	−1.17233e11	−	2.03053e11i	−0.288419	−	0.499556i
$381$	4.84446e10	−	8.39086e10i	0.117783	−	0.204007i
$382$	3.59272e11	−	6.22278e11i	0.863254	−	1.49520i
$383$	1.01055e11	+	1.75033e11i	0.239974	+	0.415647i	0.960706	−	0.277566i	$-0.0895278\pi$
$383$	1.01055e11	+	1.75033e11i	0.239974	+	0.415647i	−0.720733	+	0.693213i	$0.756194\pi$
$384$	−1.00075e12			−2.34875
$385$	2.48624e8	−	1.15192e11i	0.000576727	−	0.267208i
$386$	−8.55525e11			−1.96151
$387$	1.46331e11	+	2.53452e11i	0.331617	+	0.574377i
$388$	−1.98023e11	+	3.42986e11i	−0.443582	+	0.768306i
$389$	−1.60020e11	+	2.77163e11i	−0.354325	+	0.613709i	−0.987002	−	0.160707i	$-0.948623\pi$
$389$	−1.60020e11	+	2.77163e11i	−0.354325	+	0.613709i	0.632677	+	0.774416i	$0.281956\pi$
$390$	−1.47838e11	−	2.56063e11i	−0.323590	−	0.560474i
$391$	3.47539e11			0.751982
$392$	−7.62653e11	−	3.29216e9i	−1.63132	−	0.00704195i
$393$	−2.38069e11			−0.503427
$394$	1.00723e11	+	1.74458e11i	0.210571	+	0.364719i
$395$	−3.50240e11	+	6.06633e11i	−0.723900	+	1.25383i
$396$	8.85973e10	−	1.53455e11i	0.181047	−	0.313583i
$397$	−4.42460e11	−	7.66362e11i	−0.893956	−	1.54838i	−0.835091	−	0.550112i	$-0.814585\pi$
$397$	−4.42460e11	−	7.66362e11i	−0.893956	−	1.54838i	−0.0588653	−	0.998266i	$-0.518748\pi$
$398$	−7.33452e11			−1.46520
$399$	−4.09239e8	+	1.89608e11i	−0.000808349	+	0.374522i
$400$	3.19268e10			0.0623571
$401$	−4.28707e11	−	7.42543e11i	−0.827963	−	1.43407i	−0.899633	−	0.436646i	$-0.856166\pi$
$401$	−4.28707e11	−	7.42543e11i	−0.827963	−	1.43407i	0.0716699	−	0.997428i	$-0.477167\pi$
$402$	8.36736e11	−	1.44927e12i	1.59798	−	2.76778i
$403$	−9.10811e10	+	1.57757e11i	−0.172011	+	0.297931i
$404$	6.57944e11	+	1.13959e12i	1.22878	+	2.12830i
$405$	6.73985e11			1.24481
$406$	1.27873e12	−	7.34599e11i	2.33567	−	1.34179i
$407$	1.66235e11			0.300294
$408$	−4.28315e11	−	7.41863e11i	−0.765230	−	1.32542i
$409$	6.39178e10	−	1.10709e11i	0.112945	−	0.195626i	−0.804011	−	0.594614i	$-0.797305\pi$
$409$	6.39178e10	−	1.10709e11i	0.112945	−	0.195626i	0.916956	+	0.398987i	$0.130638\pi$
$410$	4.64180e11	−	8.03983e11i	0.811257	−	1.40514i
$411$	−4.88418e11	−	8.45965e11i	−0.844313	−	1.46239i
$412$	−4.26109e10			−0.0728590
$413$	−4.68921e11	−	2.72083e11i	−0.793093	−	0.460178i
$414$	7.76968e11			1.29988
$415$	1.11033e11	+	1.92316e11i	0.183754	+	0.318272i
$416$	−1.42319e10	+	2.46504e10i	−0.0232994	+	0.0403557i
$417$	−2.76538e11	+	4.78978e11i	−0.447860	+	0.775717i
$418$	−3.94814e10	−	6.83838e10i	−0.0632556	−	0.109562i
$419$	6.77088e11			1.07320			0.536602	−	0.843836i	$-0.319708\pi$
$419$	6.77088e11			1.07320			0.536602	+	0.843836i	$0.319708\pi$
$420$	−1.46118e12	−	8.47825e11i	−2.29131	−	1.32949i
$421$	−1.15667e11			−0.179449			−0.0897246	−	0.995967i	$-0.528599\pi$
$421$	−1.15667e11			−0.179449			−0.0897246	+	0.995967i	$0.528599\pi$
$422$	4.58575e11	+	7.94275e11i	0.703889	+	1.21917i
$423$	5.02583e10	−	8.70499e10i	0.0763266	−	0.132201i
$424$	−5.44831e11	+	9.43675e11i	−0.818682	+	1.41800i
$425$	−1.76069e10	−	3.04960e10i	−0.0261777	−	0.0453412i
$426$	2.37134e12			3.48859
$427$	−4.42457e11	+	2.54181e11i	−0.644089	+	0.370014i
$428$	−4.88454e10			−0.0703601
$429$	−3.29100e10	−	5.70019e10i	−0.0469106	−	0.0812515i
$430$	−5.80988e11	+	1.00630e12i	−0.819519	+	1.41945i
$431$	−4.40552e10	+	7.63058e10i	−0.0614964	+	0.106515i	−0.895134	−	0.445796i	$-0.852921\pi$
$431$	−4.40552e10	+	7.63058e10i	−0.0614964	+	0.106515i	0.833638	+	0.552311i	$0.186254\pi$
$432$	1.13255e11	+	1.96163e11i	0.156451	+	0.270981i
$433$	−1.12043e12			−1.53176			−0.765881	−	0.642983i	$-0.777697\pi$
$433$	−1.12043e12			−1.53176			−0.765881	+	0.642983i	$0.777697\pi$
$434$	−3.39844e9	+	1.57456e12i	−0.00459807	+	2.13037i
$435$	1.59126e12			2.13079
$436$	1.89649e11	+	3.28482e11i	0.251340	+	0.435334i
$437$	1.14431e11	−	1.98201e11i	0.150099	−	0.259979i
$438$	−5.94796e9	+	1.03022e10i	−0.00772208	+	0.0133750i
$439$	1.38720e11	+	2.40270e11i	0.178258	+	0.308752i	0.941284	−	0.337616i	$-0.109621\pi$
$439$	1.38720e11	+	2.40270e11i	0.178258	+	0.308752i	−0.763026	+	0.646368i	$0.776287\pi$
$440$	3.42713e11			0.435907
$441$	2.83788e11	+	4.96472e11i	0.357290	+	0.625059i
$442$	−2.73429e11			−0.340757
$443$	7.78420e11	+	1.34826e12i	0.960279	+	1.66325i	0.721796	+	0.692105i	$0.243317\pi$
$443$	7.78420e11	+	1.34826e12i	0.960279	+	1.66325i	0.238483	+	0.971147i	$0.423350\pi$
$444$	1.21895e12	−	2.11128e12i	1.48854	−	2.57823i
$445$	3.02519e11	−	5.23977e11i	0.365706	−	0.633421i
$446$	−4.47138e11	−	7.74467e11i	−0.535100	−	0.926821i
$447$	7.21567e11			0.854856
$448$	−2.09891e9	+	9.72461e11i	−0.00246174	+	1.14057i
$449$	1.63958e12			1.90381			0.951904	−	0.306397i	$-0.0991236\pi$
$449$	1.63958e12			1.90381			0.951904	+	0.306397i	$0.0991236\pi$
$450$	−3.93625e10	−	6.81778e10i	−0.0452508	−	0.0783766i
$451$	1.03331e11	−	1.78974e11i	0.117607	−	0.203702i
$452$	−9.71967e11	+	1.68350e12i	−1.09529	+	1.89710i
$453$	8.69624e11	+	1.50623e12i	0.970264	+	1.68055i
$454$	9.62612e11			1.06341
$455$	−2.27766e11	+	1.30846e11i	−0.249136	+	0.143123i
$456$	−5.64111e11			−0.610974
$457$	−7.84290e11	−	1.35843e12i	−0.841112	−	1.45685i	−0.888956	−	0.457993i	$-0.848568\pi$
$457$	−7.84290e11	−	1.35843e12i	−0.841112	−	1.45685i	0.0478439	−	0.998855i	$-0.484765\pi$
$458$	−7.71324e11	+	1.33597e12i	−0.819110	+	1.41874i
$459$	1.24914e11	−	2.16358e11i	0.131357	−	0.227518i
$460$	1.01954e12	+	1.76590e12i	1.06168	+	1.83889i
$461$	1.53893e12			1.58696			0.793480	−	0.608597i	$-0.208267\pi$
$461$	1.53893e12			1.58696			0.793480	+	0.608597i	$0.208267\pi$
$462$	−4.92094e11	−	2.85528e11i	−0.502526	−	0.291582i
$463$	−1.00905e12			−1.02047			−0.510233	−	0.860036i	$-0.670441\pi$
$463$	−1.00905e12			−1.02047			−0.510233	+	0.860036i	$0.670441\pi$
$464$	6.67091e11	+	1.15544e12i	0.668120	+	1.15722i
$465$	−8.49501e11	+	1.47138e12i	−0.842608	+	1.45944i
$466$	8.80598e11	−	1.52524e12i	0.865049	−	1.49831i
$467$	4.16559e11	+	7.21502e11i	0.405276	+	0.701959i	0.994354	−	0.106118i	$-0.0338421\pi$
$467$	4.16559e11	+	7.21502e11i	0.405276	+	0.701959i	−0.589078	+	0.808077i	$0.700509\pi$
$468$	−4.04059e11			−0.389349
$469$	−1.28590e12	−	7.46122e11i	−1.22724	−	0.712085i
$470$	3.99088e11			0.377249
$471$	1.94528e11	+	3.36932e11i	0.182133	+	0.315463i
$472$	8.06471e11	−	1.39685e12i	0.747911	−	1.29542i
$473$	−1.29333e11	+	2.24012e11i	−0.118805	+	0.205776i
$474$	1.72982e12	+	2.99614e12i	1.57398	+	2.72621i
$475$	−2.31891e10			−0.0209008
$476$	−1.35462e12	+	7.78195e11i	−1.20944	+	0.694795i
$477$	8.17048e11			0.722628
$478$	−1.07934e12	−	1.86948e12i	−0.945658	−	1.63793i
$479$	9.39155e11	−	1.62666e12i	0.815131	−	1.41185i	−0.0941025	−	0.995563i	$-0.529998\pi$
$479$	9.39155e11	−	1.62666e12i	0.815131	−	1.41185i	0.909234	−	0.416286i	$-0.136669\pi$
$480$	−1.32739e11	+	2.29911e11i	−0.114134	+	0.197685i
$481$	−1.89533e11	−	3.28282e11i	−0.161448	−	0.279636i
$482$	−2.51251e12			−2.12029
$483$	3.55903e9	−	1.64896e12i	0.00297557	−	1.37863i
$484$	−2.19736e12			−1.82011
$485$	2.87179e11	+	4.97409e11i	0.235676	+	0.408202i
$486$	1.27652e12	−	2.21099e12i	1.03792	−	1.79773i
$487$	−3.29534e11	+	5.70770e11i	−0.265473	+	0.459812i	−0.967687	−	0.252153i	$-0.918861\pi$
$487$	−3.29534e11	+	5.70770e11i	−0.265473	+	0.459812i	0.702215	+	0.711965i	$0.252195\pi$
$488$	−7.59064e11	−	1.31474e12i	−0.605884	−	1.04942i
$489$	−2.80682e12			−2.21985
$490$	−1.14372e12	+	1.96138e12i	−0.896267	+	1.53702i
$491$	2.13306e12			1.65629			0.828145	−	0.560514i	$-0.189396\pi$
$491$	2.13306e12			1.65629			0.828145	+	0.560514i	$0.189396\pi$
$492$	−1.51538e12	−	2.62472e12i	−1.16595	−	2.01948i
$493$	7.35769e11	−	1.27439e12i	0.560958	−	0.971607i
$494$	−9.00299e10	+	1.55936e11i	−0.0680167	+	0.117808i
$495$	−1.28486e11	−	2.22545e11i	−0.0961908	−	0.166607i
$496$	−1.42451e12			−1.05682
$497$	4.54689e9	−	2.10666e12i	0.00334281	−	1.54878i
$498$	1.09678e12			0.799076
$499$	−1.66148e11	−	2.87777e11i	−0.119962	−	0.207780i	0.799791	−	0.600279i	$-0.204944\pi$
$499$	−1.66148e11	−	2.87777e11i	−0.119962	−	0.207780i	−0.919752	+	0.392499i	$0.871611\pi$
$500$	−1.30816e12	+	2.26580e12i	−0.936043	+	1.62127i
$501$	8.83907e11	−	1.53097e12i	0.626811	−	1.08567i
$502$	1.88103e12	+	3.25804e12i	1.32199	+	2.28976i
$503$	3.41335e11			0.237752			0.118876	−	0.992909i	$-0.462071\pi$
$503$	3.41335e11			0.237752			0.118876	+	0.992909i	$0.462071\pi$
$504$	−1.47525e12	+	8.47496e11i	−1.01842	+	0.585059i
$505$	1.90834e12			1.30570
$506$	3.43358e11	+	5.94714e11i	0.232847	+	0.403302i
$507$	−7.50452e10	+	1.29982e11i	−0.0504414	+	0.0873670i
$508$	2.62849e11	−	4.55268e11i	0.175114	−	0.303306i
$509$	−2.88600e11	−	4.99870e11i	−0.190575	−	0.330086i	0.754866	−	0.655879i	$-0.227702\pi$
$509$	−2.88600e11	−	4.99870e11i	−0.190575	−	0.330086i	−0.945441	+	0.325793i	$0.894369\pi$
$510$	−2.55024e12			−1.66922
$511$	9.14087e9	+	5.30382e9i	0.00593053	+	0.00344108i
$512$	−2.38382e12			−1.53306
$513$	−8.22590e10	−	1.42477e11i	−0.0524391	−	0.0908272i
$514$	−1.95107e12	+	3.37936e12i	−1.23293	+	2.13550i
$515$	−3.08978e10	+	5.35165e10i	−0.0193551	+	0.0335240i
$516$	1.89672e12	+	3.28521e12i	1.17782	+	2.04005i
$517$	8.88406e10			0.0546895
$518$	−2.83403e12	−	1.64440e12i	−1.72950	−	1.00351i
$519$	−3.44157e12			−2.08211
$520$	−3.90747e11	−	6.76793e11i	−0.234358	−	0.405920i
$521$	−8.48706e11	+	1.47000e12i	−0.504647	+	0.874074i	0.495339	+	0.868700i	$0.335044\pi$
$521$	−8.48706e11	+	1.47000e12i	−0.504647	+	0.874074i	−0.999986	+	0.00537413i	$0.998289\pi$
$522$	1.64491e12	−	2.84906e12i	0.969671	−	1.67952i
$523$	−8.93201e11	−	1.54707e12i	−0.522025	−	0.904174i	−0.999672	−	0.0256221i	$-0.991843\pi$
$523$	−8.93201e11	−	1.54707e12i	−0.522025	−	0.904174i	0.477646	−	0.878552i	$-0.341490\pi$
$524$	−1.29171e12			−0.748467
$525$	−1.44874e11	+	8.32269e10i	−0.0832290	+	0.0478131i
$526$	−8.17941e11			−0.465893
$527$	7.85585e11	+	1.36067e12i	0.443655	+	0.768433i
$528$	2.57358e11	−	4.45756e11i	0.144107	−	0.249600i
$529$	−9.46000e10	+	1.63852e11i	−0.0525219	+	0.0909706i
$530$	1.62199e12	+	2.80938e12i	0.892910	+	1.54657i
$531$	−1.20941e12			−0.660161
$532$	−2.22043e9	+	1.02877e12i	−0.00120181	+	0.556819i
$533$	−4.71252e11			−0.252918
$534$	−1.49413e12	−	2.58791e12i	−0.795157	−	1.37725i
$535$	−3.54185e10	+	6.13466e10i	−0.0186912	+	0.0323742i
$536$	2.21156e12	−	3.83053e12i	1.15733	−	2.00455i
$537$	9.67752e11	+	1.67620e12i	0.502204	+	0.869842i
$538$	5.27645e12			2.71532
$539$	−2.54602e11	+	4.36621e11i	−0.129931	+	0.222820i
$540$	1.46580e12			0.741825
$541$	−1.20628e12	−	2.08934e12i	−0.605425	−	1.04863i	−0.991984	−	0.126363i	$-0.959670\pi$
$541$	−1.20628e12	−	2.08934e12i	−0.605425	−	1.04863i	0.386559	−	0.922265i	$-0.373664\pi$
$542$	−2.13870e12	+	3.70434e12i	−1.06452	+	1.84380i
$543$	−1.78658e12	+	3.09445e12i	−0.881908	+	1.52751i
$544$	1.22752e11	+	2.12613e11i	0.0600943	+	0.104086i
$545$	5.50069e11			0.267075
$546$	−2.80010e9	+	1.29734e12i	−0.00134836	+	0.624721i
$547$	−2.45624e11			−0.117308			−0.0586541	−	0.998278i	$-0.518681\pi$
$547$	−2.45624e11			−0.117308			−0.0586541	+	0.998278i	$0.518681\pi$
$548$	−2.65004e12	−	4.59000e12i	−1.25528	−	2.17421i
$549$	−5.69160e11	+	9.85814e11i	−0.267398	+	0.463148i
$550$	3.47902e10	−	6.02583e10i	0.0162115	−	0.0280792i
$551$	−4.84521e11	−	8.39216e11i	−0.223940	−	0.387875i
$552$	4.90591e12			2.24902
$553$	2.66504e12	−	1.53100e12i	1.21183	−	0.696166i
$554$	1.47066e11			0.0663315
$555$	−1.76775e12	−	3.06184e12i	−0.790866	−	1.36982i
$556$	−1.50043e12	+	2.59882e12i	−0.665854	+	1.15329i
$557$	−1.24583e12	+	2.15784e12i	−0.548416	+	0.949885i	0.449967	+	0.893045i	$0.351436\pi$
$557$	−1.24583e12	+	2.15784e12i	−0.548416	+	0.949885i	−0.998383	+	0.0568395i	$0.981898\pi$
$558$	1.75628e12	+	3.04196e12i	0.766901	+	1.32831i
$559$	5.89840e11			0.255494
$560$	−1.77670e12	−	1.03090e12i	−0.763428	−	0.442965i
$561$	−5.67706e11			−0.241986
$562$	−2.70050e11	−	4.67741e11i	−0.114191	−	0.197784i
$563$	8.37564e11	−	1.45070e12i	0.351342	−	0.608542i	−0.635143	−	0.772395i	$-0.719059\pi$
$563$	8.37564e11	−	1.45070e12i	0.351342	−	0.608542i	0.986485	+	0.163853i	$0.0523921\pi$
$564$	6.51441e11	−	1.12833e12i	0.271093	−	0.469548i
$565$	1.40958e12	+	2.44146e12i	0.581929	+	1.00793i
$566$	4.65148e11			0.190510
$567$	−2.55786e12	−	1.48415e12i	−1.03933	−	0.603052i
$568$	6.26762e12			2.52659
$569$	−2.09460e12	−	3.62795e12i	−0.837713	−	1.45096i	−0.891802	−	0.452426i	$-0.850559\pi$
$569$	−2.09460e12	−	3.62795e12i	−0.837713	−	1.45096i	0.0540888	−	0.998536i	$-0.482775\pi$
$570$	−8.39696e11	+	1.45440e12i	−0.333185	+	0.577093i
$571$	2.03784e12	−	3.52964e12i	0.802246	−	1.38953i	−0.115889	−	0.993262i	$-0.536972\pi$
$571$	2.03784e12	−	3.52964e12i	0.802246	−	1.38953i	0.918135	−	0.396268i	$-0.129695\pi$
$572$	−1.78562e11	−	3.09278e11i	−0.0697440	−	0.120800i
$573$	−3.40194e12			−1.31835
$574$	−3.53203e12	+	2.02907e12i	−1.35807	+	0.780177i
$575$	2.01669e11			0.0769367
$576$	1.08469e12	+	1.87874e12i	0.410587	+	0.711158i
$577$	1.26197e12	−	2.18579e12i	0.473976	−	0.820951i	−0.525580	−	0.850744i	$-0.676152\pi$
$577$	1.26197e12	−	2.18579e12i	0.473976	−	0.820951i	0.999556	+	0.0297933i	$0.00948489\pi$
$578$	1.12515e12	−	1.94881e12i	0.419308	−	0.726264i
$579$	2.02523e12	+	3.50781e12i	0.748896	+	1.29713i
$580$	8.63381e12			3.16794
$581$	2.10301e9	−	9.74363e11i	0.000765684	−	0.354755i
$582$	2.83674e12			1.02486
$583$	3.61070e11	+	6.25392e11i	0.129444	+	0.224204i
$584$	−1.57209e10	+	2.72294e10i	−0.00559267	+	0.00968680i
$585$	−2.92989e11	+	5.07472e11i	−0.103431	+	0.179147i
$586$	−1.43539e12	−	2.48617e12i	−0.502842	−	0.870948i
$587$	2.21014e12			0.768331			0.384166	−	0.923264i	$-0.374489\pi$
$587$	2.21014e12			0.768331			0.384166	+	0.923264i	$0.374489\pi$
$588$	3.67842e12	+	6.43521e12i	1.26901	+	2.22006i
$589$	1.03465e12			0.354222
$590$	−2.40091e12	−	4.15850e12i	−0.815723	−	1.41287i
$591$	4.76874e11	−	8.25969e11i	0.160790	−	0.278497i
$592$	1.48216e12	−	2.56717e12i	0.495960	−	0.859028i
$593$	−2.43833e12	−	4.22332e12i	−0.809743	−	1.40252i	−0.913042	−	0.407866i	$-0.866273\pi$
$593$	−2.43833e12	−	4.22332e12i	−0.809743	−	1.40252i	0.103299	−	0.994650i	$-0.467060\pi$
$594$	4.93647e11			0.162696
$595$	−4.88993e9	+	2.26559e12i	−0.00159947	+	0.741063i
$596$	3.91505e12			1.27095
$597$	1.73626e12	+	3.00729e12i	0.559409	+	0.968926i
$598$	7.82964e11	−	1.35613e12i	0.250372	−	0.433658i
$599$	2.35563e12	−	4.08007e12i	0.747630	−	1.29493i	−0.201326	−	0.979524i	$-0.564525\pi$
$599$	2.35563e12	−	4.08007e12i	0.747630	−	1.29493i	0.948956	−	0.315409i	$-0.102142\pi$
$600$	−2.48541e11	−	4.30486e11i	−0.0782921	−	0.135606i
$601$	−3.29323e12			−1.02964			−0.514822	−	0.857297i	$-0.672142\pi$
$601$	−3.29323e12			−1.02964			−0.514822	+	0.857297i	$0.672142\pi$
$602$	4.42085e12	−	2.53967e12i	1.37190	−	0.788122i
$603$	−3.31653e12			−1.02154
$604$	4.71837e12	+	8.17246e12i	1.44253	+	2.49854i
$605$	−1.59334e12	+	2.75974e12i	−0.483513	+	0.837469i
$606$	4.71261e12	−	8.16248e12i	1.41950	−	2.45864i
$607$	−1.74496e12	−	3.02236e12i	−0.521719	−	0.903644i	−0.999681	−	0.0252631i	$-0.991958\pi$
$607$	−1.74496e12	−	3.02236e12i	−0.521719	−	0.903644i	0.477962	−	0.878381i	$-0.341376\pi$
$608$	1.61670e11			0.0479804
$609$	−6.03905e12	−	3.50405e12i	−1.77906	−	1.03227i
$610$	−4.51956e12			−1.32164
$611$	−1.01292e11	−	1.75443e11i	−0.0294029	−	0.0509273i
$612$	−1.74253e12	+	3.01815e12i	−0.502109	+	0.869679i
$613$	−3.21047e12	+	5.56071e12i	−0.918327	+	1.59059i	−0.116370	+	0.993206i	$0.537126\pi$
$613$	−3.21047e12	+	5.56071e12i	−0.918327	+	1.59059i	−0.801957	+	0.597382i	$0.796208\pi$
$614$	−3.50052e12	−	6.06308e12i	−0.993974	−	1.72161i
$615$	−4.39530e12			−1.23894
$616$	−1.30064e12	−	7.54673e11i	−0.363952	−	0.211176i
$617$	−1.13491e12			−0.315266			−0.157633	−	0.987498i	$-0.550386\pi$
$617$	−1.13491e12			−0.315266			−0.157633	+	0.987498i	$0.550386\pi$
$618$	1.52603e11	+	2.64316e11i	0.0420838	+	0.0728913i
$619$	2.04432e12	−	3.54087e12i	0.559683	−	0.969399i	−0.437840	−	0.899053i	$-0.644256\pi$
$619$	2.04432e12	−	3.54087e12i	0.559683	−	0.969399i	0.997523	−	0.0703460i	$-0.0224103\pi$
$620$	−4.60919e12	+	7.98335e12i	−1.25274	+	2.16981i
$621$	7.15383e11	+	1.23908e12i	0.193031	+	0.334339i
$622$	1.25478e13			3.36132
$623$	−2.30192e12	+	1.32240e12i	−0.612201	+	0.351695i
$624$	−1.17371e12			−0.309906
$625$	2.03673e12	+	3.52772e12i	0.533916	+	0.924770i
$626$	−5.81313e12	+	1.00686e13i	−1.51295	+	2.62051i
$627$	−1.86924e11	+	3.23762e11i	−0.0483015	+	0.0836607i
$628$	1.05546e12	+	1.82811e12i	0.270785	+	0.469013i
$629$	−3.26949e12			−0.832823
$630$	−1.09321e10	+	5.06502e12i	−0.00276484	+	1.28100i
$631$	−5.65706e12			−1.42056			−0.710279	−	0.703921i	$-0.751431\pi$
$631$	−5.65706e12			−1.42056			−0.710279	+	0.703921i	$0.751431\pi$
$632$	4.57205e12	+	7.91903e12i	1.13995	+	1.97445i
$633$	2.17112e12	−	3.76048e12i	0.537485	−	0.930951i
$634$	−8.83401e11	+	1.53010e12i	−0.217148	+	0.376112i
$635$	−3.81191e11	−	6.60243e11i	−0.0930382	−	0.161147i
$636$	1.05905e13			2.56660
$637$	1.15253e12	+	4.97513e9i	0.277348	+	0.00119723i
$638$	2.90767e12			0.694788
$639$	−2.34979e12	−	4.06995e12i	−0.557538	−	0.965685i
$640$	−3.93727e12	+	6.81955e12i	−0.927652	+	1.60674i
$641$	−3.58997e12	+	6.21802e12i	−0.839905	+	1.45476i	0.0500685	+	0.998746i	$0.484056\pi$
$641$	−3.58997e12	+	6.21802e12i	−0.839905	+	1.45476i	−0.889973	+	0.456012i	$0.849277\pi$
$642$	1.74931e11	+	3.02989e11i	0.0406405	+	0.0703913i
$643$	−3.05769e11			−0.0705415			−0.0352708	−	0.999378i	$-0.511229\pi$
$643$	−3.05769e11			−0.0705415			−0.0352708	+	0.999378i	$0.511229\pi$
$644$	1.93105e10	−	8.94688e12i	0.00442391	−	2.04968i
$645$	5.50135e12			1.25156
$646$	7.76518e11	+	1.34497e12i	0.175430	+	0.303854i
$647$	1.87904e12	−	3.25459e12i	0.421567	−	0.730175i	−0.574526	−	0.818486i	$-0.694814\pi$
$647$	1.87904e12	−	3.25459e12i	0.421567	−	0.730175i	0.996093	+	0.0883111i	$0.0281470\pi$
$648$	4.39913e12	−	7.61951e12i	0.980119	−	1.69762i
$649$	−5.34465e11	−	9.25720e11i	−0.118255	−	0.204823i
$650$	−1.58665e11			−0.0348635
$651$	6.46402e12	−	3.71342e12i	1.41055	−	0.810326i
$652$	−1.52291e13			−3.30035
$653$	−1.45301e12	−	2.51668e12i	−0.312722	−	0.541650i	0.666229	−	0.745748i	$-0.267908\pi$
$653$	−1.45301e12	−	2.51668e12i	−0.312722	−	0.541650i	−0.978951	+	0.204097i	$0.934574\pi$
$654$	1.35839e12	−	2.35280e12i	0.290351	−	0.502903i
$655$	−9.36634e11	+	1.62230e12i	−0.198831	+	0.344386i
$656$	−1.84260e12	−	3.19148e12i	−0.388476	−	0.672860i
$657$	2.35756e10			0.00493650
$658$	−1.51459e12	−	8.78813e11i	−0.314977	−	0.182760i
$659$	1.99018e12			0.411062			0.205531	−	0.978651i	$-0.434108\pi$
$659$	1.99018e12			0.411062			0.205531	+	0.978651i	$0.434108\pi$
$660$	−1.66542e12	−	2.88460e12i	−0.341646	−	0.591749i
$661$	2.72962e12	−	4.72784e12i	0.556155	−	0.963288i	−0.441658	−	0.897183i	$-0.645610\pi$
$661$	2.72962e12	−	4.72784e12i	0.556155	−	0.963288i	0.997813	−	0.0661046i	$-0.0210571\pi$
$662$	5.00315e12	−	8.66571e12i	1.01247	−	1.75365i
$663$	6.47273e11	+	1.12111e12i	0.130100	+	0.225339i
$664$	2.89888e12			0.578727
$665$	1.29045e12	+	7.48762e11i	0.255885	+	0.148473i
$666$	−7.30938e12			−1.43962
$667$	4.21374e12	+	7.29842e12i	0.824331	+	1.42778i
$668$	4.79587e12	−	8.30669e12i	0.931908	−	1.61411i
$669$	−2.11697e12	+	3.66670e12i	−0.408599	+	0.707714i
$670$	−6.58394e12	−	1.14037e13i	−1.26226	−	2.18630i
$671$	−1.00609e12			−0.191596
$672$	1.01004e12	−	5.80243e11i	0.191063	−	0.109761i
$673$	−2.46764e12			−0.463675			−0.231838	−	0.972754i	$-0.574474\pi$
$673$	−2.46764e12			−0.463675			−0.231838	+	0.972754i	$0.574474\pi$
$674$	−2.25132e12	−	3.89940e12i	−0.420211	−	0.727827i
$675$	7.24849e10	−	1.25548e11i	0.0134394	−	0.0232778i
$676$	−4.07177e11	+	7.05251e11i	−0.0749934	+	0.129892i
$677$	3.84784e12	+	6.66465e12i	0.703992	+	1.21935i	0.967054	+	0.254571i	$0.0819343\pi$
$677$	3.84784e12	+	6.66465e12i	0.703992	+	1.21935i	−0.263062	+	0.964779i	$0.584732\pi$
$678$	1.39237e13			2.53058
$679$	5.43927e9	−	2.52011e12i	0.000982035	−	0.454994i
$680$	−6.74047e12			−1.20893
$681$	−2.27873e12	−	3.94688e12i	−0.406005	−	0.703222i
$682$	−1.55227e12	+	2.68861e12i	−0.274750	+	0.475881i
$683$	−1.01876e12	+	1.76455e12i	−0.179135	+	0.310270i	−0.941584	−	0.336777i	$-0.890663\pi$
$683$	−1.01876e12	+	1.76455e12i	−0.179135	+	0.310270i	0.762450	+	0.647048i	$0.223996\pi$
$684$	1.14750e12	+	1.98752e12i	0.200447	+	0.347184i
$685$	−7.68633e12			−1.33386
$686$	8.65962e12	−	4.92515e12i	1.49293	−	0.849104i
$687$	7.30364e12			1.25093
$688$	2.30628e12	+	3.99460e12i	0.392432	+	0.679713i
$689$	8.23353e11	−	1.42609e12i	0.139187	−	0.241079i
$690$	7.30260e12	−	1.26485e13i	1.22647	−	2.12431i
$691$	3.88640e12	+	6.73145e12i	0.648480	+	1.12320i	0.983486	+	0.180984i	$0.0579283\pi$
$691$	3.88640e12	+	6.73145e12i	0.648480	+	1.12320i	−0.335006	+	0.942216i	$0.608738\pi$
$692$	−1.86731e13			−3.09556
$693$	−2.43358e9	+	1.12752e12i	−0.000400817	+	0.185705i
$694$	−3.84842e12			−0.629745
$695$	2.17597e12	+	3.76888e12i	0.353769	+	0.612747i
$696$	1.03862e13	−	1.79895e13i	1.67771	−	2.90588i
$697$	−2.03230e12	+	3.52005e12i	−0.326167	+	0.564938i
$698$	−6.22407e12	−	1.07804e13i	−0.992488	−	1.71904i
$699$	−8.33835e12			−1.32109
$700$	−7.86054e11	+	4.51569e11i	−0.123740	+	0.0710858i
$701$	3.64001e12			0.569340			0.284670	−	0.958626i	$-0.408116\pi$
$701$	3.64001e12			0.569340			0.284670	+	0.958626i	$0.408116\pi$
$702$	−5.62834e11	−	9.74858e11i	−0.0874709	−	0.151504i
$703$	−1.07652e12	+	1.86459e12i	−0.166235	+	0.287928i
$704$	−9.58696e11	+	1.66051e12i	−0.147097	+	0.254780i
$705$	−9.44738e11	−	1.63633e12i	−0.144032	−	0.249472i
$706$	4.51646e12			0.684190
$707$	−7.24238e12	−	4.20226e12i	−1.09017	−	0.632551i
$708$	−1.56763e13			−2.34473
$709$	4.12256e12	+	7.14048e12i	0.612716	+	1.06125i	0.990781	+	0.135476i	$0.0432562\pi$
$709$	4.12256e12	+	7.14048e12i	0.612716	+	1.06125i	−0.378065	+	0.925779i	$0.623410\pi$
$710$	9.32954e12	−	1.61592e13i	1.37784	−	2.38648i
$711$	3.42821e12	−	5.93783e12i	0.503100	−	0.871395i
$712$	−3.94910e12	−	6.84004e12i	−0.575888	−	0.997467i
$713$	−8.99808e12			−1.30391
$714$	9.67847e12	+	5.61576e12i	1.39369	+	0.808660i
$715$	−5.17912e11			−0.0741103
$716$	5.25079e12	+	9.09464e12i	0.746648	+	1.29323i
$717$	−5.11013e12	+	8.85101e12i	−0.722098	+	1.25071i
$718$	−5.84957e12	+	1.01317e13i	−0.821417	+	1.42274i
$719$	4.86008e12	+	8.41790e12i	0.678209	+	1.17469i	0.975520	+	0.219911i	$0.0705768\pi$
$719$	4.86008e12	+	8.41790e12i	0.678209	+	1.17469i	−0.297311	+	0.954781i	$0.596090\pi$
$720$	−4.58237e12			−0.635468
$721$	2.35107e11	−	1.35063e11i	0.0324009	−	0.0186135i
$722$	−1.15178e13			−1.57744
$723$	5.94771e12	+	1.03017e13i	0.809520	+	1.40213i
$724$	−9.69355e12	+	1.67897e13i	−1.31117	+	2.27102i
$725$	4.26950e11	−	7.39499e11i	0.0573926	−	0.0994069i
$726$	7.86943e12	+	1.36303e13i	1.05130	+	1.82091i
$727$	−1.03185e13			−1.36997			−0.684983	−	0.728559i	$-0.740190\pi$
$727$	−1.03185e13			−1.36997			−0.684983	+	0.728559i	$0.740190\pi$
$728$	−7.40088e9	+	3.42896e12i	−0.000976545	+	0.452451i
$729$	−2.92426e12			−0.383479
$730$	4.68021e10	+	8.10635e10i	0.00609975	+	0.0105651i
$731$	2.54372e12	−	4.40585e12i	0.329489	−	0.570691i
$732$	−7.37738e12	+	1.27780e13i	−0.949734	+	1.64499i
$733$	2.79180e12	+	4.83555e12i	0.357205	+	0.618697i	0.987493	−	0.157665i	$-0.0503965\pi$
$733$	2.79180e12	+	4.83555e12i	0.357205	+	0.618697i	−0.630288	+	0.776361i	$0.717063\pi$
$734$	−2.42998e13			−3.09008
$735$	1.07495e13	+	4.64024e10i	1.35861	+	0.00586472i
$736$	−1.40600e12			−0.176618
$737$	−1.46564e12	−	2.53857e12i	−0.182989	−	0.316946i
$738$	−4.54347e12	+	7.86953e12i	−0.563812	+	0.976551i
$739$	−4.49602e11	+	7.78734e11i	−0.0554534	+	0.0960482i	−0.892420	−	0.451207i	$-0.850994\pi$
$739$	−4.49602e11	+	7.78734e11i	−0.0554534	+	0.0960482i	0.836966	+	0.547255i	$0.184327\pi$
$740$	−9.59140e12	−	1.66128e13i	−1.17582	−	2.03657i
$741$	8.52490e11			0.103874
$742$	3.07211e10	−	1.42336e13i	0.00372066	−	1.72385i
$743$	−8.04626e12			−0.968600			−0.484300	−	0.874902i	$-0.660926\pi$
$743$	−8.04626e12			−0.968600			−0.484300	+	0.874902i	$0.660926\pi$
$744$	1.10894e13	+	1.92075e13i	1.32688	+	2.29822i
$745$	2.83886e12	−	4.91705e12i	0.337630	−	0.584792i
$746$	−5.32380e12	+	9.22110e12i	−0.629357	+	1.09008i
$747$	−1.08682e12	−	1.88242e12i	−0.127707	−	0.221194i
$748$	−3.08023e12			−0.359771
$749$	2.69506e11	−	1.54825e11i	0.0312896	−	0.0179751i
$750$	1.87397e13			2.16266
$751$	−2.79237e12	−	4.83654e12i	−0.320327	−	0.554823i	0.660228	−	0.751065i	$-0.270460\pi$
$751$	−2.79237e12	−	4.83654e12i	−0.320327	−	0.554823i	−0.980556	+	0.196242i	$0.937126\pi$
$752$	7.92108e11	−	1.37197e12i	0.0903242	−	0.156446i
$753$	8.90571e12	−	1.54251e13i	1.00947	−	1.74844i
$754$	−3.31520e12	−	5.74210e12i	−0.373542	−	0.646993i
$755$	1.36854e13			1.53284
$756$	−5.56288e12	−	3.22776e12i	−0.619372	−	0.359379i
$757$	−4.47465e12			−0.495253			−0.247627	−	0.968856i	$-0.579651\pi$
$757$	−4.47465e12			−0.495253			−0.247627	+	0.968856i	$0.579651\pi$
$758$	8.86011e12	+	1.53462e13i	0.974827	+	1.68845i
$759$	1.62562e12	−	2.81566e12i	0.177800	−	0.307959i
$760$	−2.21938e12	+	3.84408e12i	−0.241307	+	0.417957i
$761$	2.41549e12	+	4.18376e12i	0.261081	+	0.452205i	0.966529	−	0.256556i	$-0.0825877\pi$
$761$	2.41549e12	+	4.18376e12i	0.261081	+	0.452205i	−0.705449	+	0.708761i	$0.749254\pi$
$762$	−3.76538e12			−0.404587
$763$	−2.08758e12	−	1.21128e12i	−0.222989	−	0.129385i
$764$	−1.84581e13			−1.96005
$765$	2.52706e12	+	4.37700e12i	0.266772	+	0.462062i
$766$	3.92728e12	−	6.80225e12i	0.412157	−	0.713876i
$767$	−1.21875e12	+	2.11093e12i	−0.127155	+	0.220239i
$768$	1.22353e13	+	2.11922e13i	1.26908	+	2.19812i
$769$	1.48019e13			1.52633			0.763167	−	0.646202i	$-0.223643\pi$
$769$	1.48019e13			1.52633			0.763167	+	0.646202i	$0.223643\pi$
$770$	−3.88175e12	+	2.22997e12i	−0.397941	+	0.228608i
$771$	1.84746e13			1.88292
$772$	1.09884e13	+	1.90325e13i	1.11342	+	1.92849i
$773$	6.06369e12	−	1.05026e13i	0.610842	−	1.05801i	−0.380257	−	0.924881i	$-0.624164\pi$
$773$	6.06369e12	−	1.05026e13i	0.610842	−	1.05801i	0.991099	−	0.133128i	$-0.0425023\pi$
$774$	5.68681e12	−	9.84985e12i	0.569554	−	0.986496i
$775$	4.55857e11	+	7.89568e11i	0.0453912	+	0.0786198i
$776$	7.49771e12			0.742251
$777$	−3.34819e10	+	1.55127e13i	−0.00329545	+	1.52684i
$778$	1.24377e13			1.21711
$779$	1.33832e12	+	2.31804e12i	0.130209	+	0.225529i
$780$	−3.79769e12	+	6.57778e12i	−0.367361	+	0.636288i
$781$	2.07684e12	−	3.59719e12i	0.199744	−	0.345966i
$782$	−6.75315e12	−	1.16968e13i	−0.645767	−	1.11850i
$783$	6.05811e12			0.575982
$784$	4.47271e12	+	7.82478e12i	0.422813	+	0.739690i
$785$	3.06132e12			0.287737
$786$	4.62601e12	+	8.01248e12i	0.432320	+	0.748799i
$787$	2.40753e12	−	4.16997e12i	0.223710	−	0.387478i	−0.732221	−	0.681067i	$-0.761516\pi$
$787$	2.40753e12	−	4.16997e12i	0.223710	−	0.387478i	0.955932	+	0.293589i	$0.0948497\pi$
$788$	2.58740e12	−	4.48151e12i	0.239054	−	0.414054i
$789$	1.93626e12	+	3.35371e12i	0.177876	+	0.308091i
$790$	2.72226e13			2.48661
$791$	2.66979e10	−	1.23696e13i	0.00242484	−	1.12347i
$792$	−3.35454e12			−0.302949
$793$	1.14710e12	+	1.98684e12i	0.103009	+	0.178416i
$794$	−1.71952e13	+	2.97829e13i	−1.53538	+	2.65935i
$795$	7.67930e12	−	1.33009e13i	0.681820	−	1.18095i
$796$	9.42052e12	+	1.63168e13i	0.831699	+	1.44054i
$797$	−1.28812e12			−0.113082			−0.0565412	−	0.998400i	$-0.518007\pi$
$797$	−1.28812e12			−0.113082			−0.0565412	+	0.998400i	$0.518007\pi$
$798$	6.38941e12	−	3.67056e12i	0.557761	−	0.320420i
$799$	−1.74731e12			−0.151674
$800$	7.12302e10	+	1.23374e11i	0.00614836	+	0.0106493i
$801$	−2.96111e12	+	5.12879e12i	−0.254160	+	0.440218i
$802$	−1.66607e13	+	2.88572e13i	−1.42203	+	2.46303i
$803$	1.04186e10	+	1.80455e10i	0.000884276	+	0.00153161i
$804$	−4.29884e13			−3.62827
$805$	−1.12227e13	−	6.51177e12i	−0.941924	−	0.546534i
$806$	7.07932e12			0.590859
$807$	−1.24906e13	−	2.16344e13i	−1.03670	−	1.79562i
$808$	1.24558e13	−	2.15741e13i	1.02806	−	1.78066i
$809$	6.09213e12	−	1.05519e13i	0.500035	−	0.866086i	−0.499965	−	0.866046i	$-0.666654\pi$
$809$	6.09213e12	−	1.05519e13i	0.500035	−	0.866086i	1.00000		4.04908e-5i	$-1.28886e-5\pi$
$810$	−1.30965e13	−	2.26837e13i	−1.06898	−	1.85154i
$811$	1.12282e13			0.911412			0.455706	−	0.890130i	$-0.349387\pi$
$811$	1.12282e13			0.911412			0.455706	+	0.890130i	$0.349387\pi$
$812$	−3.27664e13	−	1.90121e13i	−2.64501	−	1.53472i
$813$	2.02513e13			1.62572
$814$	−3.23017e12	−	5.59481e12i	−0.257878	−	0.446659i
$815$	−1.10429e13	+	1.91268e13i	−0.876742	+	1.51856i
$816$	−5.06170e12	+	8.76711e12i	−0.399660	+	0.692231i
$817$	−1.67510e12	−	2.90136e12i	−0.131535	−	0.227825i
$818$	−4.96804e12			−0.387967
$819$	2.22941e12	−	1.28074e12i	0.173146	−	0.0994682i
$820$	−2.38478e13			−1.84199
$821$	1.12196e13	+	1.94329e13i	0.861853	+	1.49277i	0.870138	+	0.492808i	$0.164029\pi$
$821$	1.12196e13	+	1.94329e13i	0.861853	+	1.49277i	−0.00828504	+	0.999966i	$0.502637\pi$
$822$	−1.89813e13	+	3.28765e13i	−1.45011	+	2.51167i
$823$	−1.58996e11	+	2.75389e11i	−0.0120805	+	0.0209241i	−0.872002	−	0.489501i	$-0.837179\pi$
$823$	−1.58996e11	+	2.75389e11i	−0.0120805	+	0.0209241i	0.859922	+	0.510426i	$0.170512\pi$
$824$	4.03342e11	+	6.98608e11i	0.0304790	+	0.0527912i
$825$	−3.29427e11			−0.0247580
$826$	−4.54742e10	+	2.10690e13i	−0.00339903	+	1.57483i
$827$	−2.12748e13			−1.58158			−0.790789	−	0.612089i	$-0.790329\pi$
$827$	−2.12748e13			−1.58158			−0.790789	+	0.612089i	$0.790329\pi$
$828$	−9.97945e12	−	1.72849e13i	−0.737853	−	1.27800i
$829$	−6.64295e12	+	1.15059e13i	−0.488501	+	0.846109i	−0.999913	−	0.0132273i	$-0.995790\pi$
$829$	−6.64295e12	+	1.15059e13i	−0.488501	+	0.846109i	0.511411	+	0.859336i	$0.329123\pi$
$830$	4.31506e12	−	7.47391e12i	0.315599	−	0.546634i
$831$	−3.48142e11	−	6.02999e11i	−0.0253251	−	0.0438644i
$832$	4.37225e12			0.316337
$833$	5.00751e12	−	8.58743e12i	0.360345	−	0.617961i
$834$	2.14941e13			1.53841
$835$	−6.95510e12	−	1.20466e13i	−0.495125	−	0.857581i
$836$	−1.01420e12	+	1.75665e12i	−0.0718120	+	0.124382i
$837$	−3.23414e12	+	5.60169e12i	−0.227769	+	0.394507i
$838$	−1.31568e13	−	2.27882e13i	−0.921617	−	1.59629i
$839$	−9.36507e11			−0.0652503			−0.0326251	−	0.999468i	$-0.510387\pi$
$839$	−9.36507e11			−0.0652503			−0.0326251	+	0.999468i	$0.510387\pi$
$840$	−6.90270e10	+	3.19814e13i	−0.00478368	+	2.21637i
$841$	2.11763e13			1.45971
$842$	2.24758e12	+	3.89292e12i	0.154103	+	0.266913i
$843$	−1.27855e12	+	2.21451e12i	−0.0871953	+	0.151027i
$844$	1.17800e13	−	2.04035e13i	0.799103	−	1.38409i
$845$	5.90500e11	+	1.02278e12i	0.0398442	+	0.0690121i
$846$	−3.90635e12			−0.262183
$847$	1.21240e13	−	6.96494e12i	0.809413	−	0.464989i
$848$	1.28773e13			0.855152
$849$	−1.10112e12	−	1.90719e12i	−0.0727359	−	0.125982i
$850$	−6.84251e11	+	1.18516e12i	−0.0449604	+	0.0778737i
$851$	9.36219e12	−	1.62158e13i	0.611920	−	1.05988i
$852$	−3.04576e13	−	5.27542e13i	−1.98024	−	3.42988i
$853$	−1.26422e13			−0.817621			−0.408810	−	0.912619i	$-0.634056\pi$
$853$	−1.26422e13			−0.817621			−0.408810	+	0.912619i	$0.634056\pi$
$854$	1.71523e13	+	9.95230e12i	1.10347	+	0.640270i
$855$	3.32826e12			0.212995
$856$	4.62355e11	+	8.00823e11i	0.0294336	+	0.0509805i
$857$	−3.48578e12	+	6.03755e12i	−0.220743	+	0.382338i	−0.955034	−	0.296497i	$-0.904182\pi$
$857$	−3.48578e12	+	6.03755e12i	−0.220743	+	0.382338i	0.734291	+	0.678835i	$0.237515\pi$
$858$	−1.27897e12	+	2.21525e12i	−0.0805692	+	0.139550i
$859$	1.02546e13	+	1.77614e13i	0.642611	+	1.11304i	0.984848	+	0.173422i	$0.0554824\pi$
$859$	1.02546e13	+	1.77614e13i	0.642611	+	1.11304i	−0.342236	+	0.939614i	$0.611184\pi$
$860$	2.98490e13			1.86075
$861$	1.66807e13	+	9.67868e12i	1.03443	+	0.600208i
$862$	3.42421e12			0.211241
$863$	−2.51068e12	−	4.34863e12i	−0.154079	−	0.266872i	0.778644	−	0.627465i	$-0.215908\pi$
$863$	−2.51068e12	−	4.34863e12i	−0.154079	−	0.266872i	−0.932723	+	0.360593i	$0.882574\pi$
$864$	−5.05352e11	+	8.75296e11i	−0.0308519	+	0.0534371i
$865$	−1.35402e13	+	2.34522e13i	−0.822339	+	1.42433i
$866$	2.17716e13	+	3.77095e13i	1.31541	+	2.27835i
$867$	−1.06540e13			−0.640362
$868$	3.50722e13	−	2.01481e13i	2.09713	−	1.20475i
$869$	6.05999e12			0.360481
$870$	−3.09204e13	−	5.35558e13i	−1.82982	−	3.16934i
$871$	−3.34212e12	+	5.78873e12i	−0.196762	+	0.340802i
$872$	3.59032e12	−	6.21862e12i	0.210285	−	0.364225i
$873$	−2.81096e12	−	4.86872e12i	−0.163791	−	0.283695i
$874$	−8.89423e12			−0.515593
$875$	3.59324e10	−	1.66481e13i	0.00207228	−	0.960126i
$876$	3.05584e11			0.0175333
$877$	−5.30070e12	−	9.18109e12i	−0.302577	−	0.524078i	0.674142	−	0.738602i	$-0.264513\pi$
$877$	−5.30070e12	−	9.18109e12i	−0.302577	−	0.524078i	−0.976719	+	0.214523i	$0.931180\pi$
$878$	5.39104e12	−	9.33755e12i	0.306159	−	0.530283i
$879$	−6.79585e12	+	1.17707e13i	−0.383967	+	0.665050i
$880$	−2.02504e12	−	3.50748e12i	−0.113831	−	0.197162i
$881$	−2.99444e13			−1.67465			−0.837324	−	0.546707i	$-0.815881\pi$
$881$	−2.99444e13			−1.67465			−0.837324	+	0.546707i	$0.815881\pi$
$882$	1.11949e13	−	1.91983e13i	0.622892	−	1.06821i
$883$	3.50061e13			1.93785			0.968927	−	0.247349i	$-0.0795593\pi$
$883$	3.50061e13			1.93785			0.968927	+	0.247349i	$0.0795593\pi$
$884$	3.51195e12	+	6.08287e12i	0.193425	+	0.335022i
$885$	−1.13671e13	+	1.96884e13i	−0.622880	+	1.07886i
$886$	3.02516e13	−	5.23972e13i	1.64929	−	2.85665i
$887$	1.36289e12	+	2.36059e12i	0.0739271	+	0.128045i	0.900619	−	0.434609i	$-0.143113\pi$
$887$	1.36289e12	+	2.36059e12i	0.0739271	+	0.128045i	−0.826692	+	0.562655i	$0.809780\pi$
$888$	−4.61527e13			−2.49080
$889$	−7.21990e9	+	3.34511e12i	−0.000387680	+	0.179619i
$890$	−2.35134e13			−1.25620
$891$	−2.91539e12	−	5.04960e12i	−0.154970	−	0.268415i
$892$	−1.14862e13	+	1.98946e13i	−0.607482	+	1.05219i
$893$	−5.75324e11	+	9.96490e11i	−0.0302748	+	0.0524374i
$894$	−1.40210e13	−	2.42852e13i	−0.734111	−	1.27152i
$895$	1.52297e13			0.793391
$896$	2.99594e13	−	1.72110e13i	1.55291	−	0.892112i
$897$	−7.41386e12			−0.382365
$898$	−3.18592e13	−	5.51818e13i	−1.63490	−	2.83173i
$899$	−1.90497e13	+	3.29950e13i	−0.972679	+	1.68473i
$900$	−1.01115e12	+	1.75136e12i	−0.0513717	+	0.0889784i
$901$	−7.10151e12	−	1.23002e13i	−0.358996	−	0.621799i
$902$	−8.03142e12			−0.403983
$903$	−2.08783e13	−	1.21143e13i	−1.04496	−	0.606321i
$904$	3.68014e13			1.83276
$905$	1.40579e13	+	2.43489e13i	0.696628	+	1.20660i
$906$	3.37960e13	−	5.85364e13i	1.66643	−	2.88635i
$907$	1.24514e13	−	2.15665e13i	0.610922	−	1.05815i	−0.380163	−	0.924919i	$-0.624132\pi$
$907$	1.24514e13	−	2.15665e13i	0.610922	−	1.05815i	0.991085	−	0.133229i	$-0.0425345\pi$
$908$	−1.23639e13	−	2.14148e13i	−0.603626	−	1.04551i
$909$	−1.86792e13			−0.907444
$910$	8.82956e12	+	5.12319e12i	0.426828	+	0.247659i
$911$	2.86750e13			1.37934			0.689670	−	0.724124i	$-0.257756\pi$
$911$	2.86750e13			1.37934			0.689670	+	0.724124i	$0.257756\pi$
$912$	3.33325e12	+	5.77336e12i	0.159548	+	0.276345i
$913$	9.60572e11	−	1.66376e12i	0.0457521	−	0.0792450i
$914$	−3.04797e13	+	5.27923e13i	−1.44462	+	2.50215i
$915$	1.06989e13	+	1.85310e13i	0.504596	+	0.873985i
$916$	3.96278e13			1.85982
$917$	7.12703e12	−	4.09431e12i	0.332849	−	0.191214i
$918$	−9.70902e12			−0.451215
$919$	−1.23115e13	−	2.13242e13i	−0.569366	−	0.986170i	−0.996629	−	0.0820431i	$-0.973855\pi$
$919$	−1.23115e13	−	2.13242e13i	−0.569366	−	0.986170i	0.427263	−	0.904127i	$-0.359478\pi$
$920$	1.93013e13	−	3.34309e13i	0.888263	−	1.53852i
$921$	−1.65732e13	+	2.87056e13i	−0.758992	+	1.31461i
$922$	−2.99036e13	−	5.17946e13i	−1.36281	−	2.36045i
$923$	−9.47168e12			−0.429556
$924$	−3.15437e10	+	1.46148e13i	−0.00142360	+	0.659581i
$925$	−1.89721e12			−0.0852076
$926$	1.96072e13	+	3.39607e13i	0.876328	+	1.51785i
$927$	3.02433e11	−	5.23829e11i	0.0134515	−	0.0232987i
$928$	−2.97662e12	+	5.15566e12i	−0.131752	+	0.228201i
$929$	1.85525e13	+	3.21338e13i	0.817204	+	1.41544i	0.907734	+	0.419546i	$0.137811\pi$
$929$	1.85525e13	+	3.21338e13i	0.817204	+	1.41544i	−0.0905297	+	0.995894i	$0.528856\pi$
$930$	6.60279e13			2.89437
$931$	−3.24862e12	−	5.68329e12i	−0.141718	−	0.247928i
$932$	−4.52419e13			−1.96412
$933$	−2.97036e13	−	5.14482e13i	−1.28334	−	2.22281i
$934$	1.61886e13	−	2.80395e13i	0.696064	−	1.20562i
$935$	−2.23352e12	+	3.86857e12i	−0.0955736	+	0.165538i
$936$	3.82470e12	+	6.62457e12i	0.162876	+	0.282109i
$937$	−2.69875e12			−0.114376			−0.0571880	−	0.998363i	$-0.518213\pi$
$937$	−2.69875e12			−0.114376			−0.0571880	+	0.998363i	$0.518213\pi$
$938$	−1.24702e11	+	5.77767e13i	−0.00525970	+	2.43691i
$939$	5.50443e13			2.31056
$940$	−5.12592e12	−	8.87836e12i	−0.214139	−	0.370900i
$941$	6.46801e11	−	1.12029e12i	0.0268916	−	0.0465777i	−0.852266	−	0.523108i	$-0.824772\pi$
$941$	6.46801e11	−	1.12029e12i	0.0268916	−	0.0465777i	0.879158	+	0.476530i	$0.158106\pi$
$942$	7.55989e12	−	1.30941e13i	0.312814	−	0.541810i
$943$	−1.16390e13	−	2.01593e13i	−0.479305	−	0.830181i
$944$	−1.90613e13			−0.781228
$945$	−8.08758e12	+	4.64612e12i	−0.329895	+	0.189517i
$946$	1.00525e13			0.408097
$947$	2.22670e13	+	3.85676e13i	0.899678	+	1.55829i	0.827906	+	0.560868i	$0.189532\pi$
$947$	2.22670e13	+	3.85676e13i	0.899678	+	1.55829i	0.0717729	+	0.997421i	$0.477134\pi$
$948$	4.44360e13	−	7.69654e13i	1.78689	−	3.09498i
$949$	2.37576e10	−	4.11493e10i	0.000950832	−	0.00164689i
$950$	4.50596e11	+	7.80455e11i	0.0179486	+	0.0310879i
$951$	8.36489e12			0.331626
$952$	2.55809e13	+	1.48429e13i	1.00937	+	0.585668i
$953$	−8.71931e12			−0.342424			−0.171212	−	0.985234i	$-0.554768\pi$
$953$	−8.71931e12			−0.342424			−0.171212	+	0.985234i	$0.554768\pi$
$954$	−1.58764e13	−	2.74987e13i	−0.620559	−	1.07484i
$955$	−1.33842e13	+	2.31822e13i	−0.520689	+	0.901859i
$956$	−2.77264e13	+	4.80234e13i	−1.07357	+	1.85949i
$957$	−6.88316e12	−	1.19220e13i	−0.265268	−	0.459457i
$958$	−7.29963e13			−2.79999
$959$	2.91706e13	+	1.69257e13i	1.11368	+	0.646194i
$960$	4.07794e13			1.54960
$961$	−7.11967e12	−	1.23316e13i	−0.269280	−	0.466407i
$962$	−7.36579e12	+	1.27579e13i	−0.277288	+	0.480277i
$963$	3.46682e11	−	6.00471e11i	0.0129901	−	0.0224996i
$964$	3.22709e13	+	5.58948e13i	1.20355	+	2.08461i
$965$	3.18715e13			1.18312
$966$	−5.55669e13	+	3.19218e13i	−2.05314	+	1.17948i
$967$	4.61060e13			1.69566			0.847828	−	0.530271i	$-0.177910\pi$
$967$	4.61060e13			1.69566			0.847828	+	0.530271i	$0.177910\pi$
$968$	2.07995e13	+	3.60258e13i	0.761402	+	1.31879i
$969$	3.67641e12	−	6.36773e12i	0.133957	−	0.232021i
$970$	1.11606e13	−	1.93307e13i	0.404775	−	0.701090i
$971$	−3.82165e11	−	6.61929e11i	−0.0137964	−	0.0238960i	0.859045	−	0.511900i	$-0.171058\pi$
$971$	−3.82165e11	−	6.61929e11i	−0.0137964	−	0.0238960i	−0.872841	+	0.488004i	$0.837725\pi$
$972$	−6.55827e13			−2.35663
$973$	4.12136e10	−	1.90950e13i	0.00147412	−	0.682985i
$974$	2.56132e13			0.911903
$975$	3.75598e11	+	6.50555e11i	0.0133108	+	0.0230549i
$976$	−8.97039e12	+	1.55372e13i	−0.316437	+	0.548085i
$977$	−1.45754e13	+	2.52453e13i	−0.511794	+	0.886453i	0.488113	+	0.872780i	$0.337685\pi$
$977$	−1.45754e13	+	2.52453e13i	−0.511794	+	0.886453i	−0.999907	+	0.0136720i	$0.995648\pi$
$978$	5.45403e13	+	9.44666e13i	1.90631	+	3.30182i
$979$	−5.23429e12			−0.182111
$980$	5.83241e13	+	2.51768e11i	2.01990	+	0.00871934i
$981$	−5.38418e12			−0.185613
$982$	−4.14483e13	−	7.17905e13i	−1.42234	−	2.46357i
$983$	−1.42476e13	+	2.46775e13i	−0.486687	+	0.842967i	−0.999883	−	0.0153046i	$-0.995128\pi$
$983$	−1.42476e13	+	2.46775e13i	−0.486687	+	0.842967i	0.513196	+	0.858272i	$0.328462\pi$
$984$	−2.86883e13	+	4.96895e13i	−0.975498	+	1.68961i
$985$	−3.75232e12	−	6.49922e12i	−0.127010	−	0.219988i
$986$	−5.71880e13			−1.92690
$987$	−1.78937e10	+	8.29046e12i	−0.000600167	+	0.278068i
$988$	4.62541e12			0.154434
$989$	1.45679e13	+	2.52323e13i	0.484186	+	0.838635i
$990$	−4.99333e12	+	8.64871e12i	−0.165208	+	0.286149i
$991$	−2.95222e11	+	5.11339e11i	−0.00972337	+	0.0168414i	−0.870846	−	0.491556i	$-0.836428\pi$
$991$	−2.95222e11	+	5.11339e11i	−0.00972337	+	0.0168414i	0.861123	+	0.508397i	$0.169762\pi$
$992$	−3.17816e12	−	5.50473e12i	−0.104201	−	0.180482i
$993$	−4.73747e13			−1.54623
$994$	−7.09902e13	+	4.07822e13i	−2.30653	+	1.32505i
$995$	2.73238e13			0.883767
$996$	−1.40872e13	−	2.43997e13i	−0.453582	−	0.785628i
$997$	5.16288e12	−	8.94237e12i	0.165487	−	0.286632i	−0.771341	−	0.636422i	$-0.780414\pi$
$997$	5.16288e12	−	8.94237e12i	0.165487	−	0.286632i	0.936828	+	0.349790i	$0.113747\pi$
$998$	−6.45696e12	+	1.11838e13i	−0.206035	+	0.356863i
$999$	−6.73002e12	−	1.16567e13i	−0.213782	−	0.370282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.e.a.53.2	✓	70
7.2	even	3	inner	91.10.e.a.79.2	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.e.a.53.2	✓	70	1.1	even	1	trivial
91.10.e.a.79.2	yes	70	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.4314 - 33.6561i) q^{2} +(-91.9975 + 159.344i) q^{3} +(-499.156 + 864.564i) q^{4} +(723.891 + 1253.82i) q^{5} +7150.55 q^{6} +(13.7108 - 6352.43i) q^{7} +18899.4 q^{8} +(-7085.57 - 12272.6i) q^{9} +O(q^{10})\)	\(q+(-19.4314 - 33.6561i) q^{2} +(-91.9975 + 159.344i) q^{3} +(-499.156 + 864.564i) q^{4} +(723.891 + 1253.82i) q^{5} +7150.55 q^{6} +(13.7108 - 6352.43i) q^{7} +18899.4 q^{8} +(-7085.57 - 12272.6i) q^{9} +(28132.4 - 48726.7i) q^{10} +(6262.52 - 10847.0i) q^{11} +(-91842.2 - 159075. i) q^{12} -28561.0 q^{13} +(-214065. + 122975. i) q^{14} -266385. q^{15} +(-111674. - 193425. i) q^{16} +(-123171. + 213338. i) q^{17} +(-275365. + 476946. i) q^{18} +(81111.0 + 140488. i) q^{19} -1.44534e6 q^{20} +(1.01096e6 + 586593. i) q^{21} -486757. q^{22} +(-705399. - 1.22179e6i) q^{23} +(-1.73870e6 + 3.01152e6i) q^{24} +(-71473.3 + 123795. i) q^{25} +(554979. + 961252. i) q^{26} -1.01415e6 q^{27} +(5.48524e6 + 3.18271e6i) q^{28} -5.97356e6 q^{29} +(5.17622e6 + 8.96547e6i) q^{30} +(3.18900e6 - 5.52352e6i) q^{31} +(498300. - 863080. i) q^{32} +(1.15227e6 + 1.99579e6i) q^{33} +9.57352e6 q^{34} +(7.97471e6 - 4.58128e6i) q^{35} +1.41472e7 q^{36} +(6.63609e6 + 1.14940e7i) q^{37} +(3.15220e6 - 5.45976e6i) q^{38} +(2.62754e6 - 4.55103e6i) q^{39} +(1.36811e7 + 2.36964e7i) q^{40} +1.64998e7 q^{41} +(98039.4 - 4.54234e7i) q^{42} -2.06519e7 q^{43} +(6.25195e6 + 1.08287e7i) q^{44} +(1.02584e7 - 1.77680e7i) q^{45} +(-2.74137e7 + 4.74820e7i) q^{46} +(3.54652e6 + 6.14275e6i) q^{47} +4.10949e7 q^{48} +(-4.03532e7 - 174193. i) q^{49} +5.55530e6 q^{50} +(-2.26628e7 - 3.92532e7i) q^{51} +(1.42564e7 - 2.46928e7i) q^{52} +(-2.88279e7 + 4.99314e7i) q^{53} +(1.97064e7 + 3.41325e7i) q^{54} +1.81335e7 q^{55} +(259126. - 1.20057e8i) q^{56} -2.98480e7 q^{57} +(1.16074e8 + 2.01047e8i) q^{58} +(4.26717e7 - 7.39096e7i) q^{59} +(1.32968e8 - 2.30306e8i) q^{60} +(-4.01633e7 - 6.95649e7i) q^{61} -2.47867e8 q^{62} +(-7.80579e7 + 4.48424e7i) q^{63} -1.53085e8 q^{64} +(-2.06750e7 - 3.58102e7i) q^{65} +(4.47805e7 - 7.75620e7i) q^{66} +(1.17017e8 - 2.02680e8i) q^{67} +(-1.22963e8 - 2.12978e8i) q^{68} +2.59580e8 q^{69} +(-3.09148e8 - 1.79377e8i) q^{70} +3.31630e8 q^{71} +(-1.33913e8 - 2.31945e8i) q^{72} +(-831818. + 1.44075e6i) q^{73} +(2.57897e8 - 4.46690e8i) q^{74} +(-1.31507e7 - 2.27777e7i) q^{75} -1.61948e8 q^{76} +(-6.88190e7 - 3.99310e7i) q^{77} -2.04227e8 q^{78} +(2.41915e8 + 4.19009e8i) q^{79} +(1.61680e8 - 2.80037e8i) q^{80} +(2.32765e8 - 4.03161e8i) q^{81} +(-3.20614e8 - 5.55320e8i) q^{82} +1.53384e8 q^{83} +(-1.01178e9 + 5.81241e8i) q^{84} -3.56649e8 q^{85} +(4.01295e8 + 6.95064e8i) q^{86} +(5.49552e8 - 9.51853e8i) q^{87} +(1.18358e8 - 2.05002e8i) q^{88} +(-2.08953e8 - 3.61917e8i) q^{89} -7.97336e8 q^{90} +(-391593. + 1.81432e8i) q^{91} +1.40842e9 q^{92} +(5.86760e8 + 1.01630e9i) q^{93} +(1.37828e8 - 2.38724e8i) q^{94} +(-1.17431e8 + 2.03397e8i) q^{95} +(9.16846e7 + 1.58802e8i) q^{96} +3.96716e8 q^{97} +(7.78256e8 + 1.36152e9i) q^{98} -1.77494e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9}+O(q^{10}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9} + 16725 q^{10} + 117246 q^{11} + 79155 q^{12} - 1999270 q^{13} + 155800 q^{14} - 1075914 q^{15} - 1801693 q^{16} + 534494 q^{17} + 2034224 q^{18} - 1070554 q^{19} - 213462 q^{20} + 252483 q^{21} - 656508 q^{22} + 3982482 q^{23} - 8713082 q^{24} - 10791923 q^{25} - 1856465 q^{26} - 4695462 q^{27} + 43151747 q^{28} - 8248096 q^{29} + 7494360 q^{30} - 18116139 q^{31} + 23284165 q^{32} - 18685134 q^{33} - 35031796 q^{34} + 41739462 q^{35} + 69822756 q^{36} + 12174052 q^{37} - 86227130 q^{38} - 45752120 q^{40} - 14899440 q^{41} + 226294688 q^{42} - 100872292 q^{43} + 55709994 q^{44} - 128782765 q^{45} + 86862955 q^{46} - 15243502 q^{47} - 251600258 q^{48} + 168431298 q^{49} - 23415484 q^{50} + 89493887 q^{51} + 243711013 q^{52} + 42576150 q^{53} - 466420190 q^{54} - 72659096 q^{55} + 237491061 q^{56} - 533277320 q^{57} + 302514895 q^{58} + 40301350 q^{59} - 191686454 q^{60} + 9519912 q^{61} - 257610720 q^{62} - 292394291 q^{63} + 453888112 q^{64} + 60492198 q^{65} + 1445199979 q^{66} + 919692072 q^{67} - 220295462 q^{68} - 1381257496 q^{69} + 860352188 q^{70} - 811959580 q^{71} + 2266117080 q^{72} + 924540004 q^{73} - 727436321 q^{74} + 445426010 q^{75} + 649412196 q^{76} - 1151937348 q^{77} - 495761838 q^{78} + 1174788834 q^{79} + 2332520349 q^{80} - 800698791 q^{81} + 1124625342 q^{82} + 830514540 q^{83} + 1448184376 q^{84} - 1969339174 q^{85} + 1497823546 q^{86} + 721368044 q^{87} - 808482999 q^{88} - 1968216306 q^{89} + 777819470 q^{90} + 250308604 q^{91} - 4887921618 q^{92} + 853972744 q^{93} + 4664723138 q^{94} + 1357929150 q^{95} - 3736344295 q^{96} + 3467931764 q^{97} - 1557173329 q^{98} - 8781494080 q^{99}+O(q^{100}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9 + 16725 * q^10 + 117246 * q^11 + 79155 * q^12 - 1999270 * q^13 + 155800 * q^14 - 1075914 * q^15 - 1801693 * q^16 + 534494 * q^17 + 2034224 * q^18 - 1070554 * q^19 - 213462 * q^20 + 252483 * q^21 - 656508 * q^22 + 3982482 * q^23 - 8713082 * q^24 - 10791923 * q^25 - 1856465 * q^26 - 4695462 * q^27 + 43151747 * q^28 - 8248096 * q^29 + 7494360 * q^30 - 18116139 * q^31 + 23284165 * q^32 - 18685134 * q^33 - 35031796 * q^34 + 41739462 * q^35 + 69822756 * q^36 + 12174052 * q^37 - 86227130 * q^38 - 45752120 * q^40 - 14899440 * q^41 + 226294688 * q^42 - 100872292 * q^43 + 55709994 * q^44 - 128782765 * q^45 + 86862955 * q^46 - 15243502 * q^47 - 251600258 * q^48 + 168431298 * q^49 - 23415484 * q^50 + 89493887 * q^51 + 243711013 * q^52 + 42576150 * q^53 - 466420190 * q^54 - 72659096 * q^55 + 237491061 * q^56 - 533277320 * q^57 + 302514895 * q^58 + 40301350 * q^59 - 191686454 * q^60 + 9519912 * q^61 - 257610720 * q^62 - 292394291 * q^63 + 453888112 * q^64 + 60492198 * q^65 + 1445199979 * q^66 + 919692072 * q^67 - 220295462 * q^68 - 1381257496 * q^69 + 860352188 * q^70 - 811959580 * q^71 + 2266117080 * q^72 + 924540004 * q^73 - 727436321 * q^74 + 445426010 * q^75 + 649412196 * q^76 - 1151937348 * q^77 - 495761838 * q^78 + 1174788834 * q^79 + 2332520349 * q^80 - 800698791 * q^81 + 1124625342 * q^82 + 830514540 * q^83 + 1448184376 * q^84 - 1969339174 * q^85 + 1497823546 * q^86 + 721368044 * q^87 - 808482999 * q^88 - 1968216306 * q^89 + 777819470 * q^90 + 250308604 * q^91 - 4887921618 * q^92 + 853972744 * q^93 + 4664723138 * q^94 + 1357929150 * q^95 - 3736344295 * q^96 + 3467931764 * q^97 - 1557173329 * q^98 - 8781494080 * q^99

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